10 126

10_125

10_127

(KnotPlot image)	See the full Rolfsen Knot Table. Visit 10 126's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 126 at Knotilus!
	10_126 is also known as the pretzel knot P(-5,3,2).

Knot presentations

Planar diagram presentation	X4251 X8493 X5,14,6,15 X15,20,16,1 X9,16,10,17 X11,18,12,19 X17,10,18,11 X19,12,20,13 X13,6,14,7 X2837
Gauss code	1, -10, 2, -1, -3, 9, 10, -2, -5, 7, -6, 8, -9, 3, -4, 5, -7, 6, -8, 4
Dowker-Thistlethwaite code	4 8 -14 2 -16 -18 -6 -20 -10 -12
Conway Notation	[41,3,2-]

Minimum Braid Representative	A Morse Link Presentation	An Arc Presentation
Length is 10, width is 3, Braid index is 3		[{3, 10}, {2, 4}, {1, 3}, {13, 11}, {10, 12}, {11, 5}, {4, 6}, {5, 7}, {6, 8}, {7, 9}, {8, 13}, {12, 2}, {9, 1}]

[edit Notes on presentations of 10 126]

Computer Talk

The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:=

AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of May 31, 2006, 14:15:20.091. Read more at http://katlas.org/wiki/KnotTheory.

In[3]:=

K = Knot["10 126"];

In[4]:=

PD[K]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

X4251 X8493 X5,14,6,15 X15,20,16,1 X9,16,10,17 X11,18,12,19 X17,10,18,11 X19,12,20,13 X13,6,14,7 X2837

In[5]:=

GaussCode[K]

Out[5]=

1, -10, 2, -1, -3, 9, 10, -2, -5, 7, -6, 8, -9, 3, -4, 5, -7, 6, -8, 4

In[6]:=

DTCode[K]

Out[6]=

4 8 -14 2 -16 -18 -6 -20 -10 -12

(The path below may be different on your system)

In[7]:=

AppendTo[$Path, "C:/bin/LinKnot/"];

In[8]:=

ConwayNotation[K]

Out[8]=

[41,3,2-]

In[9]:=

br = BR[K]

KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.

Out[9]=

${\textrm {BR}}(3,\{-1,-1,-1,-1,-1,-2,1,1,1,-2\})$

In[10]:=

{First[br], Crossings[br], BraidIndex[K]}

KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.

KnotTheory::loading: Loading precomputed data in IndianaData`.

Out[10]=

{ 3, 10, 3 }

In[11]:=

Show[BraidPlot[br]]

Out[11]=

-Graphics-

In[12]:=

Show[DrawMorseLink[K]]

KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."

KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."

Out[12]=

-Graphics-

In[13]:=

ap = ArcPresentation[K]

Out[13]=

ArcPresentation[{3, 10}, {2, 4}, {1, 3}, {13, 11}, {10, 12}, {11, 5}, {4, 6}, {5, 7}, {6, 8}, {7, 9}, {8, 13}, {12, 2}, {9, 1}]

In[14]:=

Draw[ap]

Out[14]=

-Graphics-

Three dimensional invariants

Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-10][0] Hyperbolic Volume 6.90426 A-Polynomial See Data:10 126/A-polynomial

[edit Notes for 10 126's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $3$ Rasmussen s-Invariant 2

[edit Notes for 10 126's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$t^{3}-2t^{2}+4t-5+4t^{-1}-2t^{-2}+t^{-3}$
Conway polynomial	$z^{6}+4z^{4}+5z^{2}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 19, -2 }
Jones polynomial	$-1+2q^{-1}-2q^{-2}+4q^{-3}-3q^{-4}+3q^{-5}-2q^{-6}+q^{-7}-q^{-8}$
HOMFLY-PT polynomial (db, data sources)	$-z^{4}a^{6}-4z^{2}a^{6}-4a^{6}+z^{6}a^{4}+6z^{4}a^{4}+12z^{2}a^{4}+7a^{4}-z^{4}a^{2}-3z^{2}a^{2}-2a^{2}$
Kauffman polynomial (db, data sources)	$z^{5}a^{9}-4z^{3}a^{9}+3za^{9}+z^{6}a^{8}-3z^{4}a^{8}+z^{2}a^{8}+z^{7}a^{7}-3z^{5}a^{7}+2z^{3}a^{7}-za^{7}+z^{8}a^{6}-5z^{6}a^{6}+11z^{4}a^{6}-11z^{2}a^{6}+4a^{6}+2z^{7}a^{5}-9z^{5}a^{5}+16z^{3}a^{5}-8za^{5}+z^{8}a^{4}-6z^{6}a^{4}+16z^{4}a^{4}-16z^{2}a^{4}+7a^{4}+z^{7}a^{3}-5z^{5}a^{3}+11z^{3}a^{3}-6za^{3}+2z^{4}a^{2}-4z^{2}a^{2}+2a^{2}+z^{3}a-2za$
The A2 invariant	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{24}-q^{22}-2 q^{20}-q^{18}+q^{16}+q^{14}+3 q^{12}+2 q^{10}+2 q^8+q^6-q^4-1}
The G2 invariant	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{128}+q^{124}-q^{122}+q^{120}-q^{116}+2 q^{114}-2 q^{112}+2 q^{110}-2 q^{108}-3 q^{102}+4 q^{100}-5 q^{98}+q^{96}-q^{94}-4 q^{92}+3 q^{90}-5 q^{88}-q^{86}+q^{84}-5 q^{82}+2 q^{80}-2 q^{78}-4 q^{76}+6 q^{74}-5 q^{72}+3 q^{70}-3 q^{66}+6 q^{64}-4 q^{62}+5 q^{60}+2 q^{56}+4 q^{54}-2 q^{52}+7 q^{50}-q^{48}+3 q^{46}+3 q^{44}-2 q^{42}+5 q^{40}+2 q^{38}-2 q^{36}+6 q^{34}-3 q^{32}+q^{30}+2 q^{28}-5 q^{26}+5 q^{24}-4 q^{22}+q^{20}-3 q^{16}+2 q^{14}-2 q^{12}-q^8-q^4-q^2+ q^{-4} }

Further Quantum Invariants

Further quantum knot invariants for 10_126.

A1 Invariants.

Weight	Invariant
1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{17}-q^{13}+q^{11}+q^7+2 q^5+q- q^{-1} }
2	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{48}+q^{42}-q^{40}-2 q^{38}+q^{36}-3 q^{32}+q^{28}-2 q^{26}+2 q^{22}+q^{16}+3 q^{14}-q^{12}+3 q^8-q^6-q^4+2 q^2- q^{-2} }
3	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{93}+q^{83}+q^{81}-q^{77}+q^{75}+3 q^{73}+q^{71}-3 q^{69}-3 q^{67}+2 q^{65}+4 q^{63}-6 q^{59}-3 q^{57}+3 q^{55}+4 q^{53}-4 q^{51}-5 q^{49}+q^{47}+4 q^{45}-2 q^{43}-3 q^{41}+3 q^{37}-q^{31}+q^{29}+4 q^{27}-q^{25}-4 q^{23}+7 q^{19}+2 q^{17}-4 q^{15}-3 q^{13}+5 q^{11}+4 q^9-q^7-3 q^5+2 q+2 q^{-1} - q^{-3} -2 q^{-5} - q^{-7} + q^{-11} }
5	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{225}+q^{217}+q^{215}-q^{207}+2 q^{203}+q^{201}-2 q^{195}-3 q^{193}-q^{191}+2 q^{189}+3 q^{187}+3 q^{185}-5 q^{181}-8 q^{179}-5 q^{177}+q^{175}+9 q^{173}+11 q^{171}+6 q^{169}-5 q^{167}-15 q^{165}-16 q^{163}-4 q^{161}+12 q^{159}+23 q^{157}+20 q^{155}+3 q^{153}-20 q^{151}-32 q^{149}-21 q^{147}+7 q^{145}+33 q^{143}+40 q^{141}+15 q^{139}-25 q^{137}-47 q^{135}-34 q^{133}+6 q^{131}+45 q^{129}+50 q^{127}+11 q^{125}-35 q^{123}-53 q^{121}-27 q^{119}+22 q^{117}+49 q^{115}+32 q^{113}-8 q^{111}-38 q^{109}-31 q^{107}+2 q^{105}+26 q^{103}+22 q^{101}+4 q^{99}-16 q^{97}-16 q^{95}-2 q^{93}+8 q^{91}+6 q^{89}+q^{87}-4 q^{85}-6 q^{83}-q^{81}+3 q^{79}+q^{75}-3 q^{73}-8 q^{71}-8 q^{69}+q^{67}+14 q^{65}+14 q^{63}+3 q^{61}-16 q^{59}-28 q^{57}-12 q^{55}+22 q^{53}+40 q^{51}+26 q^{49}-14 q^{47}-48 q^{45}-41 q^{43}+7 q^{41}+49 q^{39}+52 q^{37}+12 q^{35}-39 q^{33}-55 q^{31}-26 q^{29}+20 q^{27}+49 q^{25}+40 q^{23}+2 q^{21}-31 q^{19}-36 q^{17}-19 q^{15}+11 q^{13}+29 q^{11}+24 q^9+6 q^7-12 q^5-20 q^3-15 q- q^{-1} +11 q^{-3} +12 q^{-5} +7 q^{-7} - q^{-9} -7 q^{-11} -8 q^{-13} -3 q^{-15} +2 q^{-17} +3 q^{-19} +3 q^{-21} + q^{-23} - q^{-25} - q^{-27} }
6	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{312}-q^{304}-q^{302}-q^{300}+q^{298}+q^{292}-q^{288}-2 q^{286}+q^{284}+q^{282}+2 q^{278}+q^{276}-3 q^{272}-q^{270}+4 q^{264}+5 q^{262}+4 q^{260}-3 q^{258}-4 q^{256}-6 q^{254}-8 q^{252}-2 q^{250}+6 q^{248}+14 q^{246}+10 q^{244}+7 q^{242}-4 q^{240}-18 q^{238}-24 q^{236}-18 q^{234}+14 q^{230}+34 q^{228}+34 q^{226}+15 q^{224}-14 q^{222}-39 q^{220}-48 q^{218}-42 q^{216}+q^{214}+43 q^{212}+70 q^{210}+64 q^{208}+25 q^{206}-36 q^{204}-93 q^{202}-93 q^{200}-49 q^{198}+30 q^{196}+100 q^{194}+127 q^{192}+79 q^{190}-25 q^{188}-113 q^{186}-146 q^{184}-96 q^{182}+11 q^{180}+127 q^{178}+166 q^{176}+100 q^{174}-21 q^{172}-133 q^{170}-165 q^{168}-98 q^{166}+39 q^{164}+142 q^{162}+148 q^{160}+65 q^{158}-53 q^{156}-130 q^{154}-120 q^{152}-26 q^{150}+69 q^{148}+105 q^{146}+72 q^{144}-60 q^{140}-73 q^{138}-29 q^{136}+20 q^{134}+43 q^{132}+34 q^{130}+8 q^{128}-15 q^{126}-25 q^{124}-11 q^{122}+3 q^{120}+8 q^{118}+5 q^{116}-q^{114}-5 q^{112}-6 q^{110}-2 q^{108}+3 q^{106}+7 q^{104}+4 q^{102}-q^{100}-9 q^{98}-16 q^{96}-20 q^{94}-7 q^{92}+24 q^{90}+34 q^{88}+31 q^{86}+2 q^{84}-39 q^{82}-70 q^{80}-52 q^{78}+19 q^{76}+79 q^{74}+104 q^{72}+57 q^{70}-38 q^{68}-128 q^{66}-135 q^{64}-42 q^{62}+77 q^{60}+161 q^{58}+142 q^{56}+32 q^{54}-110 q^{52}-179 q^{50}-131 q^{48}-12 q^{46}+117 q^{44}+171 q^{42}+125 q^{40}+2 q^{38}-108 q^{36}-143 q^{34}-105 q^{32}-10 q^{30}+83 q^{28}+123 q^{26}+88 q^{24}+18 q^{22}-47 q^{20}-87 q^{18}-77 q^{16}-27 q^{14}+27 q^{12}+54 q^{10}+55 q^8+35 q^6-3 q^4-33 q^2-39-27 q^{-2} -9 q^{-4} +9 q^{-6} +24 q^{-8} +23 q^{-10} +11 q^{-12} - q^{-14} -10 q^{-16} -13 q^{-18} -12 q^{-20} -3 q^{-22} +3 q^{-24} +5 q^{-26} +5 q^{-28} +4 q^{-30} +2 q^{-32} -2 q^{-34} - q^{-36} - q^{-38} - q^{-40} - q^{-42} + q^{-46} }

A2 Invariants.

Weight	Invariant
1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{24}-q^{22}-2 q^{20}-q^{18}+q^{16}+q^{14}+3 q^{12}+2 q^{10}+2 q^8+q^6-q^4-1}
1,1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{68}+2 q^{64}-2 q^{62}+4 q^{60}-4 q^{58}+4 q^{56}-8 q^{54}+7 q^{52}-8 q^{50}+8 q^{48}-6 q^{46}+q^{44}+2 q^{42}-10 q^{40}+10 q^{38}-18 q^{36}+14 q^{34}-18 q^{32}+12 q^{30}-13 q^{28}+10 q^{26}-2 q^{24}+6 q^{22}+10 q^{20}-2 q^{18}+16 q^{16}-6 q^{14}+10 q^{12}-8 q^{10}+2 q^8-4 q^6-q^4-2 q^2+ q^{-4} }
2,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{62}+q^{60}+2 q^{58}+2 q^{56}+2 q^{54}-q^{50}-3 q^{48}-4 q^{46}-7 q^{44}-6 q^{42}-3 q^{40}-2 q^{38}+q^{34}+4 q^{32}+3 q^{30}+4 q^{28}+4 q^{26}+5 q^{24}+2 q^{22}+3 q^{20}+q^{18}-q^{16}-q^{14}-q^8+q^4-1}

A3 Invariants.

Weight	Invariant
0,1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{54}+q^{50}+q^{48}-3 q^{40}-q^{38}-2 q^{36}-6 q^{34}-4 q^{32}-4 q^{30}-3 q^{28}+5 q^{24}+7 q^{22}+9 q^{20}+7 q^{18}+7 q^{16}+q^{14}-2 q^{12}-q^{10}-4 q^8-4 q^6+ q^{-2} }
1,0,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{31}-q^{29}-3 q^{27}-2 q^{25}-2 q^{23}+q^{21}+2 q^{19}+4 q^{17}+4 q^{15}+3 q^{13}+2 q^{11}-2 q^5-q}
1,0,1	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{88}+2 q^{84}+q^{80}+q^{78}-2 q^{76}+q^{74}-2 q^{72}-3 q^{70}+q^{68}-4 q^{66}+5 q^{64}+q^{62}+3 q^{60}+9 q^{58}-4 q^{56}+11 q^{54}-9 q^{52}-3 q^{50}-12 q^{48}-18 q^{46}-14 q^{44}-20 q^{42}-7 q^{40}-11 q^{38}+12 q^{36}+3 q^{34}+24 q^{32}+17 q^{30}+19 q^{28}+24 q^{26}+3 q^{24}+15 q^{22}-4 q^{20}-2 q^{18}-5 q^{16}-8 q^{14}-5 q^{12}-3 q^{10}-3 q^8-q^6-q^2+2+ q^{-4} }

A4 Invariants.

Weight	Invariant
0,1,0,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{68}+q^{66}+2 q^{64}+3 q^{62}+3 q^{60}+2 q^{58}+3 q^{56}-4 q^{52}-6 q^{50}-8 q^{48}-12 q^{46}-15 q^{44}-12 q^{42}-9 q^{40}-6 q^{38}+q^{36}+11 q^{34}+14 q^{32}+18 q^{30}+21 q^{28}+17 q^{26}+10 q^{24}+5 q^{22}-q^{20}-7 q^{18}-10 q^{16}-7 q^{14}-5 q^{12}-4 q^{10}-q^8+2 q^6+q^4+q^2+1}
1,0,0,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{38}-q^{36}-3 q^{34}-3 q^{32}-3 q^{30}-2 q^{28}+q^{26}+2 q^{24}+5 q^{22}+5 q^{20}+5 q^{18}+3 q^{16}+2 q^{14}-q^{10}-q^8-2 q^6-q^2}

B2 Invariants.

Weight	Invariant
0,1	$-q^{54}-q^{50}+q^{48}-2q^{46}+2q^{44}-2q^{42}+q^{40}-q^{38}-2q^{32}+2q^{30}-3q^{28}+4q^{26}-3q^{24}+5q^{22}-q^{20}+3q^{18}+q^{16}+q^{14}+2q^{12}-q^{10}+2q^{8}-2q^{6}+2q^{4}-2q^{2}-q^{-2}$
1,0	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{88}+q^{80}+q^{78}-q^{74}+q^{70}+q^{68}-2 q^{66}-3 q^{64}-q^{62}+q^{60}-q^{58}-4 q^{56}-3 q^{54}-q^{52}-q^{50}-2 q^{48}-2 q^{46}+2 q^{42}+q^{40}+q^{38}+2 q^{36}+5 q^{34}+4 q^{32}+3 q^{30}+q^{28}+4 q^{26}+3 q^{24}+q^{22}-2 q^{20}+q^{16}-3 q^{12}-3 q^{10}-q^8+q^6-q^2+ q^{-4} }

D4 Invariants.

Weight

Invariant

1,0,0,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{74}+q^{70}+2 q^{66}-q^{64}+q^{62}-2 q^{60}+q^{58}-2 q^{56}-2 q^{52}-2 q^{50}-3 q^{48}-6 q^{46}-4 q^{44}-7 q^{42}-3 q^{40}-6 q^{38}+3 q^{36}+q^{34}+10 q^{32}+7 q^{30}+12 q^{28}+8 q^{26}+9 q^{24}+5 q^{22}+q^{20}-q^{18}-4 q^{16}-2 q^{14}-5 q^{12}-2 q^{10}-4 q^8+q^6-q^4+q^2+ q^{-2} }

G2 Invariants.

Weight

Invariant

1,0

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{128}+q^{124}-q^{122}+q^{120}-q^{116}+2 q^{114}-2 q^{112}+2 q^{110}-2 q^{108}-3 q^{102}+4 q^{100}-5 q^{98}+q^{96}-q^{94}-4 q^{92}+3 q^{90}-5 q^{88}-q^{86}+q^{84}-5 q^{82}+2 q^{80}-2 q^{78}-4 q^{76}+6 q^{74}-5 q^{72}+3 q^{70}-3 q^{66}+6 q^{64}-4 q^{62}+5 q^{60}+2 q^{56}+4 q^{54}-2 q^{52}+7 q^{50}-q^{48}+3 q^{46}+3 q^{44}-2 q^{42}+5 q^{40}+2 q^{38}-2 q^{36}+6 q^{34}-3 q^{32}+q^{30}+2 q^{28}-5 q^{26}+5 q^{24}-4 q^{22}+q^{20}-3 q^{16}+2 q^{14}-2 q^{12}-q^8-q^4-q^2+ q^{-4} }

.

Computer Talk

The above data is available with the Mathematica package KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:=

AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of August 31, 2006, 11:25:27.5625. Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:=

K = Knot["10 126"];

In[4]:=

Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

$t^{3}-2t^{2}+4t-5+4t^{-1}-2t^{-2}+t^{-3}$

In[5]:=

Conway[K][z]

Out[5]=

$z^{6}+4z^{4}+5z^{2}+1$

In[6]:=

Alexander[K, 2][t]

KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.

Out[6]=

$\{1\}$

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 19, -2 }

In[8]:=

Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]=

$-1+2q^{-1}-2q^{-2}+4q^{-3}-3q^{-4}+3q^{-5}-2q^{-6}+q^{-7}-q^{-8}$

In[9]:=

HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]=

$-z^{4}a^{6}-4z^{2}a^{6}-4a^{6}+z^{6}a^{4}+6z^{4}a^{4}+12z^{2}a^{4}+7a^{4}-z^{4}a^{2}-3z^{2}a^{2}-2a^{2}$

In[10]:=

Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]=

$z^{5}a^{9}-4z^{3}a^{9}+3za^{9}+z^{6}a^{8}-3z^{4}a^{8}+z^{2}a^{8}+z^{7}a^{7}-3z^{5}a^{7}+2z^{3}a^{7}-za^{7}+z^{8}a^{6}-5z^{6}a^{6}+11z^{4}a^{6}-11z^{2}a^{6}+4a^{6}+2z^{7}a^{5}-9z^{5}a^{5}+16z^{3}a^{5}-8za^{5}+z^{8}a^{4}-6z^{6}a^{4}+16z^{4}a^{4}-16z^{2}a^{4}+7a^{4}+z^{7}a^{3}-5z^{5}a^{3}+11z^{3}a^{3}-6za^{3}+2z^{4}a^{2}-4z^{2}a^{2}+2a^{2}+z^{3}a-2za$

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q\leftrightarrow q^{-1}} ): {}

Computer Talk

The above data is available with the Mathematica package KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:=

AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of May 31, 2006, 14:15:20.091. Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:=

K = Knot["10 126"];

In[4]:=

{A = Alexander[K][t], J = Jones[K][q]}

KnotTheory::loading: Loading precomputed data in PD4Knots`.

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[4]=

{ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^3-2 t^2+4 t-5+4 t^{-1} -2 t^{-2} + t^{-3} } , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1+2 q^{-1} -2 q^{-2} +4 q^{-3} -3 q^{-4} +3 q^{-5} -2 q^{-6} + q^{-7} - q^{-8} } }

In[5]:=

DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]

KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.

KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.

Out[5]=

{}

In[6]:=

DeleteCases[ Select[ AllKnots[], (J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & ], K ]

KnotTheory::loading: Loading precomputed data in Jones4Knots11`.

Out[6]=

{}

Vassiliev invariants

V2 and V3:

(5, -9)

V2,1 through V6,9:

V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 20} $-72$ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 200} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1222}{3}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{194}{3}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1440} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2416} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -384} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -392} ${\frac {4000}{3}}$ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2592} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{24440}{3}} ${\frac {3880}{3}}$ ${\frac {87967}{6}}$ $-{\frac {310}{3}}$ ${\frac {56342}{9}}$ ${\frac {3109}{18}}$ ${\frac {5119}{6}}$

V_2,1 through V_6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V₂ and V₃.

Khovanov Homology

The coefficients of the monomials $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} ). The squares with yellow highlighting are those on the "critical diagonals", where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s+1} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s-1} , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s=} -2 is the signature of 10 126. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ -7 -6 -5 -4 -3 -2 -1 0 1 χ 1                 1 -1 -1               1   1 -3             2 2   0 -5           2       2 -7         1 2       1 -9       2 2         0 -11       1           1 -13   1 2             -1 -15                   0 -17 1                 -1

Integral Khovanov Homology (db, data source)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=-3} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=-1} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-7} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-6} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}_2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}} $r=-5$ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-4} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}\oplus{\mathbb Z}_2^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-3} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}\oplus{\mathbb Z}_2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-1} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}_2^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=0} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=1} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}_2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n+1} -dimensional representation of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sl(2)} )

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_n}
2	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1+ q^{-1} +2 q^{-2} -4 q^{-3} + q^{-4} +6 q^{-5} -7 q^{-6} +10 q^{-8} -9 q^{-9} - q^{-10} +10 q^{-11} -7 q^{-12} -3 q^{-13} +8 q^{-14} -4 q^{-15} -4 q^{-16} +5 q^{-17} - q^{-18} -3 q^{-19} +2 q^{-20} - q^{-22} + q^{-23} }
3	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^4-q^3-q^2-q+2+2 q^{-1} - q^{-2} -3 q^{-3} - q^{-4} +4 q^{-5} +4 q^{-6} -2 q^{-7} -9 q^{-8} +3 q^{-9} +10 q^{-10} +3 q^{-11} -16 q^{-12} - q^{-13} +13 q^{-14} +8 q^{-15} -19 q^{-16} -3 q^{-17} +14 q^{-18} +8 q^{-19} -16 q^{-20} -6 q^{-21} +11 q^{-22} +9 q^{-23} -10 q^{-24} -9 q^{-25} +5 q^{-26} +10 q^{-27} -2 q^{-28} -10 q^{-29} - q^{-30} +7 q^{-31} +4 q^{-32} -6 q^{-33} -3 q^{-34} +2 q^{-35} +4 q^{-36} -2 q^{-37} - q^{-38} +2 q^{-40} - q^{-41} + q^{-44} - q^{-45} }
4	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^8+q^7+2 q^6-q^4-5 q^3-q^2+5 q+4+4 q^{-1} -8 q^{-2} -10 q^{-3} +3 q^{-4} +4 q^{-5} +15 q^{-6} + q^{-7} -15 q^{-8} -7 q^{-9} -10 q^{-10} +22 q^{-11} +19 q^{-12} -7 q^{-13} -13 q^{-14} -33 q^{-15} +18 q^{-16} +34 q^{-17} +6 q^{-18} -10 q^{-19} -51 q^{-20} +11 q^{-21} +39 q^{-22} +13 q^{-23} -3 q^{-24} -60 q^{-25} +8 q^{-26} +40 q^{-27} +14 q^{-28} - q^{-29} -59 q^{-30} +6 q^{-31} +36 q^{-32} +14 q^{-33} +5 q^{-34} -54 q^{-35} +26 q^{-37} +14 q^{-38} +16 q^{-39} -41 q^{-40} -8 q^{-41} +8 q^{-42} +9 q^{-43} +27 q^{-44} -21 q^{-45} -9 q^{-46} -7 q^{-47} -3 q^{-48} +26 q^{-49} -4 q^{-50} -10 q^{-52} -11 q^{-53} +14 q^{-54} +7 q^{-56} -3 q^{-57} -9 q^{-58} +5 q^{-59} -3 q^{-60} +5 q^{-61} + q^{-62} -4 q^{-63} +3 q^{-64} -3 q^{-65} + q^{-66} + q^{-67} -2 q^{-68} +2 q^{-69} - q^{-70} - q^{-73} + q^{-74} }
5	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{11}+2 q^9+2 q^8-q^6-6 q^5-5 q^4+3 q^3+8 q^2+8 q+4-7 q^{-1} -17 q^{-2} -11 q^{-3} +3 q^{-4} +16 q^{-5} +22 q^{-6} +11 q^{-7} -12 q^{-8} -29 q^{-9} -27 q^{-10} - q^{-11} +27 q^{-12} +44 q^{-13} +26 q^{-14} -20 q^{-15} -56 q^{-16} -47 q^{-17} -2 q^{-18} +60 q^{-19} +77 q^{-20} +20 q^{-21} -59 q^{-22} -89 q^{-23} -50 q^{-24} +53 q^{-25} +111 q^{-26} +60 q^{-27} -45 q^{-28} -107 q^{-29} -84 q^{-30} +37 q^{-31} +123 q^{-32} +79 q^{-33} -34 q^{-34} -107 q^{-35} -97 q^{-36} +28 q^{-37} +123 q^{-38} +84 q^{-39} -30 q^{-40} -108 q^{-41} -94 q^{-42} +24 q^{-43} +118 q^{-44} +86 q^{-45} -25 q^{-46} -103 q^{-47} -92 q^{-48} +14 q^{-49} +104 q^{-50} +86 q^{-51} -5 q^{-52} -85 q^{-53} -88 q^{-54} -10 q^{-55} +71 q^{-56} +79 q^{-57} +25 q^{-58} -45 q^{-59} -71 q^{-60} -37 q^{-61} +22 q^{-62} +53 q^{-63} +43 q^{-64} + q^{-65} -32 q^{-66} -42 q^{-67} -17 q^{-68} +13 q^{-69} +30 q^{-70} +23 q^{-71} +8 q^{-72} -17 q^{-73} -24 q^{-74} -13 q^{-75} +2 q^{-76} +12 q^{-77} +20 q^{-78} +6 q^{-79} -7 q^{-80} -10 q^{-81} -9 q^{-82} -4 q^{-83} +8 q^{-84} +7 q^{-85} +3 q^{-86} + q^{-87} -4 q^{-88} -6 q^{-89} + q^{-91} +4 q^{-93} + q^{-94} -3 q^{-95} -3 q^{-98} +2 q^{-99} +2 q^{-100} - q^{-101} + q^{-103} -2 q^{-104} + q^{-106} + q^{-109} - q^{-110} }
6	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{20}-q^{19}-q^{18}-q^{14}+5 q^{13}+q^{12}-2 q^9-6 q^8-10 q^7+4 q^6+4 q^5+9 q^4+12 q^3+10 q^2-5 q-25-14 q^{-1} -14 q^{-2} -3 q^{-3} +18 q^{-4} +40 q^{-5} +33 q^{-6} -5 q^{-7} -15 q^{-8} -41 q^{-9} -57 q^{-10} -32 q^{-11} +30 q^{-12} +73 q^{-13} +60 q^{-14} +55 q^{-15} -6 q^{-16} -97 q^{-17} -125 q^{-18} -65 q^{-19} +35 q^{-20} +95 q^{-21} +165 q^{-22} +117 q^{-23} -51 q^{-24} -179 q^{-25} -194 q^{-26} -84 q^{-27} +47 q^{-28} +234 q^{-29} +259 q^{-30} +59 q^{-31} -160 q^{-32} -278 q^{-33} -203 q^{-34} -46 q^{-35} +241 q^{-36} +349 q^{-37} +154 q^{-38} -113 q^{-39} -303 q^{-40} -263 q^{-41} -117 q^{-42} +223 q^{-43} +380 q^{-44} +195 q^{-45} -84 q^{-46} -300 q^{-47} -273 q^{-48} -148 q^{-49} +210 q^{-50} +384 q^{-51} +202 q^{-52} -76 q^{-53} -295 q^{-54} -270 q^{-55} -152 q^{-56} +205 q^{-57} +380 q^{-58} +203 q^{-59} -72 q^{-60} -289 q^{-61} -267 q^{-62} -157 q^{-63} +191 q^{-64} +366 q^{-65} +213 q^{-66} -49 q^{-67} -263 q^{-68} -258 q^{-69} -180 q^{-70} +142 q^{-71} +322 q^{-72} +226 q^{-73} +11 q^{-74} -191 q^{-75} -225 q^{-76} -216 q^{-77} +47 q^{-78} +228 q^{-79} +216 q^{-80} +88 q^{-81} -73 q^{-82} -142 q^{-83} -222 q^{-84} -56 q^{-85} +91 q^{-86} +149 q^{-87} +120 q^{-88} +39 q^{-89} -21 q^{-90} -156 q^{-91} -95 q^{-92} -25 q^{-93} +42 q^{-94} +70 q^{-95} +72 q^{-96} +67 q^{-97} -52 q^{-98} -47 q^{-99} -52 q^{-100} -28 q^{-101} -9 q^{-102} +28 q^{-103} +67 q^{-104} +5 q^{-105} +14 q^{-106} -13 q^{-107} -22 q^{-108} -36 q^{-109} -14 q^{-110} +24 q^{-111} - q^{-112} +23 q^{-113} +12 q^{-114} +7 q^{-115} -17 q^{-116} -14 q^{-117} +4 q^{-118} -15 q^{-119} +5 q^{-120} +6 q^{-121} +13 q^{-122} -3 q^{-123} -3 q^{-124} +7 q^{-125} -11 q^{-126} -3 q^{-127} -2 q^{-128} +7 q^{-129} - q^{-130} - q^{-131} +8 q^{-132} -4 q^{-133} -2 q^{-134} -3 q^{-135} +3 q^{-136} - q^{-137} -2 q^{-138} +6 q^{-139} - q^{-140} - q^{-141} -2 q^{-142} + q^{-143} -2 q^{-145} +3 q^{-146} - q^{-149} - q^{-152} + q^{-153} }

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Rolfsen Knot Page master template (intermediate). See/edit the Rolfsen_Splice_Base (expert). Back to the top.

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