10 5

10_4

10_6

(KnotPlot image)	See the full Rolfsen Knot Table. Visit 10 5's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 5 at Knotilus!

Knot presentations

Planar diagram presentation	X1425 X3,12,4,13 X13,1,14,20 X5,15,6,14 X7,17,8,16 X9,19,10,18 X15,7,16,6 X17,9,18,8 X19,11,20,10 X11,2,12,3
Gauss code	-1, 10, -2, 1, -4, 7, -5, 8, -6, 9, -10, 2, -3, 4, -7, 5, -8, 6, -9, 3
Dowker-Thistlethwaite code	4 12 14 16 18 2 20 6 8 10
Conway Notation	[6112]

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

[edit Notes on presentations of 10 5]

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 5"];

In[4]:=

PD[K]

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

Out[4]=

X1425 X3,12,4,13 X13,1,14,20 X5,15,6,14 X7,17,8,16 X9,19,10,18 X15,7,16,6 X17,9,18,8 X19,11,20,10 X11,2,12,3

In[5]:=

GaussCode[K]

Out[5]=

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

In[6]:=

DTCode[K]

Out[6]=

4 12 14 16 18 2 20 6 8 10

(The path below may be different on your system)

In[7]:=

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

In[8]:=

ConwayNotation[K]

Out[8]=

[6112]

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]=

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

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

In[14]:=

Draw[ap]

Out[14]=

-Graphics-

Three dimensional invariants

Symmetry type Reversible Unknotting number 2 3-genus 4 Bridge index 2 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [0][-12] Hyperbolic Volume 7.37394 A-Polynomial See Data:10 5/A-polynomial

[edit Notes for 10 5's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 10 5's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$t^{4}-3t^{3}+5t^{2}-5t+5-5t^{-1}+5t^{-2}-3t^{-3}+t^{-4}$
Conway polynomial	$z^{8}+5z^{6}+7z^{4}+4z^{2}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 33, 4 }
Jones polynomial	$-q^{9}+2q^{8}-3q^{7}+4q^{6}-5q^{5}+5q^{4}-4q^{3}+4q^{2}-2q+2-q^{-1}$
HOMFLY-PT polynomial (db, data sources)	$z^{8}a^{-4}-z^{6}a^{-2}+7z^{6}a^{-4}-z^{6}a^{-6}-5z^{4}a^{-2}+17z^{4}a^{-4}-5z^{4}a^{-6}-6z^{2}a^{-2}+17z^{2}a^{-4}-7z^{2}a^{-6}-a^{-2}+5a^{-4}-3a^{-6}$
Kauffman polynomial (db, data sources)	$z^{9}a^{-3}+z^{9}a^{-5}+2z^{8}a^{-2}+4z^{8}a^{-4}+2z^{8}a^{-6}+z^{7}a^{-1}-3z^{7}a^{-3}-2z^{7}a^{-5}+2z^{7}a^{-7}-11z^{6}a^{-2}-20z^{6}a^{-4}-7z^{6}a^{-6}+2z^{6}a^{-8}-5z^{5}a^{-1}-2z^{5}a^{-3}-3z^{5}a^{-5}-4z^{5}a^{-7}+2z^{5}a^{-9}+18z^{4}a^{-2}+32z^{4}a^{-4}+10z^{4}a^{-6}-2z^{4}a^{-8}+2z^{4}a^{-10}+6z^{3}a^{-1}+7z^{3}a^{-3}+6z^{3}a^{-5}+3z^{3}a^{-7}-z^{3}a^{-9}+z^{3}a^{-11}-10z^{2}a^{-2}-22z^{2}a^{-4}-9z^{2}a^{-6}+z^{2}a^{-8}-2z^{2}a^{-10}-za^{-1}-2za^{-3}-3za^{-5}-za^{-7}-za^{-11}+a^{-2}+5a^{-4}+3a^{-6}$
The A2 invariant	$-q^{2}+q^{-4}+2q^{-6}+q^{-8}+2q^{-10}-q^{-12}+q^{-14}-q^{-22}-q^{-26}$
The G2 invariant	$q^{12}-q^{10}+2q^{8}-3q^{6}+q^{4}-2q^{2}-1+5q^{-2}-8q^{-4}+8q^{-6}-7q^{-8}+2q^{-10}+3q^{-12}-9q^{-14}+10q^{-16}-9q^{-18}+5q^{-20}+2q^{-22}-4q^{-24}+7q^{-26}-3q^{-28}+2q^{-30}+4q^{-32}-2q^{-34}+2q^{-36}+2q^{-38}-2q^{-40}+8q^{-42}-4q^{-44}+6q^{-46}-2q^{-48}-q^{-50}+7q^{-52}-10q^{-54}+9q^{-56}-6q^{-58}+2q^{-60}+2q^{-62}-6q^{-64}+6q^{-66}-5q^{-68}+2q^{-70}-3q^{-74}+q^{-76}+q^{-78}-2q^{-80}+q^{-82}-q^{-86}+2q^{-88}-2q^{-90}+q^{-92}+q^{-96}-q^{-98}-q^{-100}-q^{-104}+2q^{-106}-4q^{-108}+4q^{-110}-3q^{-112}-q^{-114}+2q^{-116}-5q^{-118}+5q^{-120}-5q^{-122}+3q^{-124}-q^{-126}-2q^{-128}+4q^{-130}-4q^{-132}+4q^{-134}-2q^{-136}+q^{-138}-2q^{-142}+2q^{-144}-q^{-146}+q^{-148}$

Further Quantum Invariants

Further quantum knot invariants for 10_5.

A1 Invariants.

Weight	Invariant
1	$-q^{3}+q+2q^{-3}+q^{-7}-q^{-11}+q^{-13}-q^{-15}+q^{-17}-q^{-19}$
2	$q^{12}-q^{10}-2q^{8}+2q^{6}-3q^{2}+2+3q^{-2}-2q^{-4}+q^{-6}+3q^{-8}+2q^{-14}-2q^{-18}+q^{-22}-q^{-24}-q^{-26}+q^{-28}-2q^{-32}+q^{-34}-q^{-38}+2q^{-40}-q^{-42}-q^{-44}+2q^{-46}-q^{-48}-q^{-50}+q^{-52}$
3	$-q^{27}+q^{25}+2q^{23}-3q^{19}-2q^{17}+4q^{15}+3q^{13}-4q^{11}-6q^{9}+q^{7}+6q^{5}+2q^{3}-6q-2q^{-1}+4q^{-3}+5q^{-5}-q^{-7}-2q^{-9}+3q^{-13}+3q^{-15}+2q^{-17}-2q^{-19}-2q^{-21}+2q^{-23}+4q^{-25}-2q^{-27}-5q^{-29}+2q^{-31}+3q^{-33}-3q^{-35}-6q^{-37}+3q^{-39}+4q^{-41}-5q^{-45}-q^{-47}+2q^{-49}+3q^{-51}+q^{-53}-5q^{-55}-4q^{-57}+4q^{-59}+6q^{-61}-q^{-63}-7q^{-65}-q^{-67}+7q^{-69}+3q^{-71}-5q^{-73}-4q^{-75}+3q^{-77}+5q^{-79}-2q^{-81}-4q^{-83}+3q^{-87}-2q^{-91}+q^{-95}+q^{-97}-q^{-99}$
4	$q^{48}-q^{46}-2q^{44}+q^{40}+5q^{38}-4q^{34}-4q^{32}-3q^{30}+10q^{28}+7q^{26}-2q^{24}-8q^{22}-13q^{20}+4q^{18}+10q^{16}+8q^{14}-16q^{10}-6q^{8}+3q^{6}+10q^{4}+9q^{2}-6-5q^{-2}-4q^{-4}+q^{-6}+6q^{-8}+5q^{-12}+3q^{-14}-2q^{-16}-4q^{-18}-7q^{-20}+8q^{-22}+15q^{-24}+4q^{-26}-9q^{-28}-18q^{-30}+q^{-32}+20q^{-34}+11q^{-36}-8q^{-38}-22q^{-40}-8q^{-42}+16q^{-44}+13q^{-46}-3q^{-48}-17q^{-50}-8q^{-52}+13q^{-54}+10q^{-56}-3q^{-58}-12q^{-60}-5q^{-62}+11q^{-64}+9q^{-66}-2q^{-68}-12q^{-70}-9q^{-72}+5q^{-74}+12q^{-76}+8q^{-78}-q^{-80}-14q^{-82}-15q^{-84}+4q^{-86}+19q^{-88}+20q^{-90}-8q^{-92}-28q^{-94}-13q^{-96}+14q^{-98}+33q^{-100}+5q^{-102}-27q^{-104}-22q^{-106}+3q^{-108}+30q^{-110}+10q^{-112}-17q^{-114}-18q^{-116}-3q^{-118}+22q^{-120}+9q^{-122}-8q^{-124}-11q^{-126}-6q^{-128}+12q^{-130}+5q^{-132}-2q^{-134}-5q^{-136}-5q^{-138}+6q^{-140}+q^{-142}-q^{-146}-2q^{-148}+3q^{-150}-q^{-156}-q^{-158}+q^{-160}$
5	$-q^{75}+q^{73}+2q^{71}-q^{67}-3q^{65}-3q^{63}+6q^{59}+6q^{57}+q^{55}-5q^{53}-10q^{51}-8q^{49}+3q^{47}+16q^{45}+15q^{43}+3q^{41}-11q^{39}-22q^{37}-15q^{35}+5q^{33}+22q^{31}+21q^{29}+7q^{27}-13q^{25}-28q^{23}-18q^{21}+3q^{19}+20q^{17}+22q^{15}+8q^{13}-11q^{11}-18q^{9}-12q^{7}+q^{5}+11q^{3}+8q-q^{-1}-q^{-3}+2q^{-5}+6q^{-7}+3q^{-9}-8q^{-11}-20q^{-13}-11q^{-15}+15q^{-17}+35q^{-19}+27q^{-21}-3q^{-23}-39q^{-25}-45q^{-27}-7q^{-29}+42q^{-31}+59q^{-33}+27q^{-35}-31q^{-37}-64q^{-39}-44q^{-41}+15q^{-43}+62q^{-45}+54q^{-47}-q^{-49}-53q^{-51}-60q^{-53}-19q^{-55}+40q^{-57}+59q^{-59}+27q^{-61}-28q^{-63}-55q^{-65}-35q^{-67}+14q^{-69}+47q^{-71}+37q^{-73}-6q^{-75}-38q^{-77}-32q^{-79}+2q^{-81}+29q^{-83}+30q^{-85}-4q^{-87}-29q^{-89}-20q^{-91}+5q^{-93}+25q^{-95}+21q^{-97}-8q^{-99}-29q^{-101}-20q^{-103}+6q^{-105}+27q^{-107}+27q^{-109}+8q^{-111}-19q^{-113}-34q^{-115}-25q^{-117}+3q^{-119}+35q^{-121}+44q^{-123}+22q^{-125}-25q^{-127}-59q^{-129}-44q^{-131}+10q^{-133}+59q^{-135}+59q^{-137}+9q^{-139}-53q^{-141}-67q^{-143}-21q^{-145}+41q^{-147}+61q^{-149}+24q^{-151}-30q^{-153}-50q^{-155}-21q^{-157}+26q^{-159}+40q^{-161}+13q^{-163}-25q^{-165}-30q^{-167}-4q^{-169}+22q^{-171}+25q^{-173}+q^{-175}-23q^{-177}-22q^{-179}+2q^{-181}+19q^{-183}+17q^{-185}+2q^{-187}-13q^{-189}-15q^{-191}-3q^{-193}+8q^{-195}+9q^{-197}+3q^{-199}-3q^{-201}-5q^{-203}-3q^{-205}+q^{-207}+3q^{-209}+q^{-211}-q^{-217}+q^{-219}-q^{-223}-q^{-225}+q^{-231}+q^{-233}-q^{-235}$
6	$q^{108}-q^{106}-2q^{104}+q^{100}+3q^{98}+q^{96}+3q^{94}-2q^{92}-8q^{90}-5q^{88}-q^{86}+6q^{84}+7q^{82}+14q^{80}+3q^{78}-12q^{76}-18q^{74}-17q^{72}-3q^{70}+6q^{68}+33q^{66}+30q^{64}+8q^{62}-15q^{60}-35q^{58}-34q^{56}-27q^{54}+19q^{52}+43q^{50}+45q^{48}+25q^{46}-8q^{44}-36q^{42}-62q^{40}-30q^{38}+3q^{36}+37q^{34}+49q^{32}+36q^{30}+8q^{28}-38q^{26}-40q^{24}-33q^{22}-3q^{20}+22q^{18}+31q^{16}+22q^{14}-10q^{12}-14q^{10}-17q^{8}+6q^{6}+20q^{4}+17q^{2}-2-40q^{-2}-43q^{-4}-26q^{-6}+31q^{-8}+74q^{-10}+75q^{-12}+32q^{-14}-53q^{-16}-107q^{-18}-109q^{-20}-25q^{-22}+77q^{-24}+142q^{-26}+136q^{-28}+29q^{-30}-94q^{-32}-173q^{-34}-136q^{-36}-23q^{-38}+105q^{-40}+189q^{-42}+143q^{-44}+18q^{-46}-122q^{-48}-178q^{-50}-139q^{-52}-22q^{-54}+122q^{-56}+177q^{-58}+131q^{-60}+5q^{-62}-108q^{-64}-170q^{-66}-137q^{-68}-4q^{-70}+114q^{-72}+165q^{-74}+113q^{-76}+6q^{-78}-119q^{-80}-176q^{-82}-100q^{-84}+26q^{-86}+133q^{-88}+152q^{-90}+85q^{-92}-52q^{-94}-157q^{-96}-132q^{-98}-31q^{-100}+85q^{-102}+138q^{-104}+105q^{-106}-10q^{-108}-116q^{-110}-113q^{-112}-41q^{-114}+49q^{-116}+94q^{-118}+75q^{-120}-4q^{-122}-76q^{-124}-67q^{-126}-12q^{-128}+46q^{-130}+61q^{-132}+30q^{-134}-30q^{-136}-67q^{-138}-45q^{-140}+9q^{-142}+60q^{-144}+70q^{-146}+38q^{-148}-22q^{-150}-68q^{-152}-83q^{-154}-48q^{-156}+16q^{-158}+77q^{-160}+103q^{-162}+75q^{-164}+7q^{-166}-95q^{-168}-143q^{-170}-115q^{-172}-11q^{-174}+106q^{-176}+177q^{-178}+153q^{-180}+8q^{-182}-130q^{-184}-206q^{-186}-148q^{-188}-10q^{-190}+145q^{-192}+220q^{-194}+132q^{-196}-9q^{-198}-152q^{-200}-182q^{-202}-116q^{-204}+25q^{-206}+142q^{-208}+137q^{-210}+79q^{-212}-31q^{-214}-89q^{-216}-107q^{-218}-53q^{-220}+22q^{-222}+46q^{-224}+70q^{-226}+41q^{-228}+17q^{-230}-32q^{-232}-49q^{-234}-40q^{-236}-34q^{-238}+17q^{-240}+40q^{-242}+57q^{-244}+22q^{-246}-11q^{-248}-35q^{-250}-53q^{-252}-18q^{-254}+8q^{-256}+41q^{-258}+30q^{-260}+14q^{-262}-6q^{-264}-31q^{-266}-18q^{-268}-12q^{-270}+11q^{-272}+13q^{-274}+13q^{-276}+7q^{-278}-7q^{-280}-4q^{-282}-11q^{-284}-q^{-286}+5q^{-290}+5q^{-292}+3q^{-296}-5q^{-298}-q^{-300}-2q^{-302}+3q^{-310}-q^{-312}+q^{-314}-q^{-320}-q^{-322}+q^{-324}$

A2 Invariants.

Weight	Invariant
1,0	$-q^{2}+q^{-4}+2q^{-6}+q^{-8}+2q^{-10}-q^{-12}+q^{-14}-q^{-22}-q^{-26}$
1,1	$q^{12}-2q^{10}+4q^{8}-8q^{6}+13q^{4}-20q^{2}+24-32q^{-2}+30q^{-4}-30q^{-6}+24q^{-8}-10q^{-10}+6q^{-12}+18q^{-14}-18q^{-16}+36q^{-18}-36q^{-20}+44q^{-22}-44q^{-24}+38q^{-26}-35q^{-28}+22q^{-30}-20q^{-32}+6q^{-34}-4q^{-36}-2q^{-38}+2q^{-40}+q^{-44}+2q^{-48}-4q^{-50}+5q^{-52}-10q^{-54}+12q^{-56}-12q^{-58}+13q^{-60}-12q^{-62}+12q^{-64}-10q^{-66}+7q^{-68}-6q^{-70}+4q^{-72}-2q^{-74}+q^{-76}$
2,0	$q^{10}-q^{6}-q^{4}-1-3q^{-2}+2q^{-6}+q^{-8}+4q^{-12}+4q^{-14}+3q^{-16}+2q^{-18}+3q^{-20}-q^{-24}-q^{-30}+q^{-34}-3q^{-36}-3q^{-38}-q^{-40}-q^{-44}-q^{-46}+q^{-48}+q^{-50}-q^{-54}+q^{-66}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{6}-q^{4}-3q^{-2}+2q^{-10}+3q^{-12}+q^{-14}+4q^{-16}+2q^{-18}+q^{-20}+4q^{-22}+2q^{-24}-q^{-26}-q^{-30}-3q^{-32}-3q^{-34}-q^{-36}-2q^{-40}+2q^{-44}-2q^{-46}-q^{-48}+3q^{-50}-q^{-52}-2q^{-54}+2q^{-56}-q^{-60}+q^{-62}$
1,0,0	$-q-q^{-3}+q^{-5}+3q^{-9}+q^{-11}+2q^{-13}+q^{-15}+q^{-17}+q^{-19}+q^{-23}-2q^{-25}-2q^{-29}-q^{-33}$
1,0,1	$q^{12}-2q^{10}+3q^{8}-3q^{6}+q^{4}+3q^{2}-6+9q^{-2}-12q^{-4}+3q^{-6}-6q^{-8}-7q^{-10}+3q^{-12}-6q^{-14}+10q^{-16}-q^{-18}+21q^{-20}-q^{-22}+26q^{-24}+2q^{-26}+11q^{-28}+14q^{-30}-16q^{-32}+17q^{-34}-23q^{-36}+7q^{-38}-20q^{-40}-10q^{-44}-10q^{-46}+7q^{-48}-19q^{-50}+17q^{-52}-12q^{-54}+9q^{-56}+3q^{-58}-2q^{-60}+6q^{-62}-2q^{-64}+2q^{-66}-5q^{-68}+6q^{-70}-8q^{-72}+4q^{-74}+2q^{-76}-7q^{-78}+11q^{-80}-7q^{-82}+2q^{-84}+4q^{-86}-8q^{-88}+6q^{-90}-3q^{-92}-q^{-94}+3q^{-96}-2q^{-98}+q^{-100}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{4}-q^{-4}-3q^{-6}-2q^{-8}-q^{-10}-q^{-12}+q^{-16}+4q^{-18}+3q^{-20}+4q^{-22}+4q^{-24}+7q^{-26}+6q^{-28}+6q^{-30}+3q^{-32}+4q^{-34}+q^{-36}-4q^{-38}-4q^{-40}-4q^{-42}-6q^{-44}-5q^{-46}-q^{-48}-3q^{-50}-2q^{-52}+q^{-54}+q^{-56}-2q^{-58}-q^{-60}+2q^{-62}-2q^{-66}+q^{-68}+2q^{-70}+q^{-76}$
1,0,0,0	$-1-q^{-4}+q^{-10}+2q^{-12}+q^{-14}+3q^{-16}+q^{-18}+3q^{-20}+q^{-22}+2q^{-24}-q^{-30}-2q^{-32}-q^{-34}-2q^{-36}-q^{-40}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{6}+q^{4}-2q^{2}+2-3q^{-2}+4q^{-4}-4q^{-6}+4q^{-8}-2q^{-10}+3q^{-12}+q^{-14}+4q^{-18}-3q^{-20}+6q^{-22}-6q^{-24}+7q^{-26}-6q^{-28}+5q^{-30}-5q^{-32}+3q^{-34}-3q^{-36}-2q^{-42}+2q^{-44}-2q^{-46}+3q^{-48}-3q^{-50}+3q^{-52}-2q^{-54}+2q^{-56}-2q^{-58}+q^{-60}-q^{-62}$
1,0	$q^{12}-q^{8}-q^{6}+q^{4}+q^{2}-2-3q^{-2}+3q^{-6}-3q^{-10}-q^{-12}+4q^{-14}+4q^{-16}+q^{-18}-3q^{-20}+q^{-22}+4q^{-24}+4q^{-26}-q^{-28}-2q^{-30}+3q^{-34}+q^{-36}-q^{-38}+2q^{-42}-2q^{-46}-q^{-48}+q^{-50}+q^{-52}-2q^{-54}-3q^{-56}-q^{-58}+2q^{-60}-2q^{-64}-2q^{-66}+q^{-68}+2q^{-70}-2q^{-74}-2q^{-76}+q^{-78}+3q^{-80}+q^{-82}-2q^{-84}-2q^{-86}+2q^{-90}+q^{-92}-q^{-94}-q^{-96}+q^{-100}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{6}-q^{4}+q^{2}-2+2q^{-2}-4q^{-4}+2q^{-6}-4q^{-8}+3q^{-10}-3q^{-12}+2q^{-14}-q^{-16}+3q^{-18}+2q^{-20}+q^{-22}+5q^{-24}+2q^{-26}+8q^{-28}+8q^{-32}-3q^{-34}+6q^{-36}-6q^{-38}+2q^{-40}-7q^{-42}-6q^{-46}-3q^{-50}-q^{-56}+q^{-58}-q^{-60}+2q^{-62}-2q^{-64}+q^{-66}-2q^{-68}+3q^{-70}-2q^{-72}+q^{-74}-2q^{-76}+2q^{-78}-q^{-80}+q^{-82}-q^{-84}+q^{-86}$

G2 Invariants.

Weight

Invariant

1,0

$q^{12}-q^{10}+2q^{8}-3q^{6}+q^{4}-2q^{2}-1+5q^{-2}-8q^{-4}+8q^{-6}-7q^{-8}+2q^{-10}+3q^{-12}-9q^{-14}+10q^{-16}-9q^{-18}+5q^{-20}+2q^{-22}-4q^{-24}+7q^{-26}-3q^{-28}+2q^{-30}+4q^{-32}-2q^{-34}+2q^{-36}+2q^{-38}-2q^{-40}+8q^{-42}-4q^{-44}+6q^{-46}-2q^{-48}-q^{-50}+7q^{-52}-10q^{-54}+9q^{-56}-6q^{-58}+2q^{-60}+2q^{-62}-6q^{-64}+6q^{-66}-5q^{-68}+2q^{-70}-3q^{-74}+q^{-76}+q^{-78}-2q^{-80}+q^{-82}-q^{-86}+2q^{-88}-2q^{-90}+q^{-92}+q^{-96}-q^{-98}-q^{-100}-q^{-104}+2q^{-106}-4q^{-108}+4q^{-110}-3q^{-112}-q^{-114}+2q^{-116}-5q^{-118}+5q^{-120}-5q^{-122}+3q^{-124}-q^{-126}-2q^{-128}+4q^{-130}-4q^{-132}+4q^{-134}-2q^{-136}+q^{-138}-2q^{-142}+2q^{-144}-q^{-146}+q^{-148}$

.

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 5"];

In[4]:=

Alexander[K][t]

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

Out[4]=

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

In[5]:=

Conway[K][z]

Out[5]=

$z^{8}+5z^{6}+7z^{4}+4z^{2}+1$

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]=

{ 33, 4 }

In[8]:=

Jones[K][q]

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

Out[8]=

$-q^{9}+2q^{8}-3q^{7}+4q^{6}-5q^{5}+5q^{4}-4q^{3}+4q^{2}-2q+2-q^{-1}$

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

$z^{8}a^{-4}-z^{6}a^{-2}+7z^{6}a^{-4}-z^{6}a^{-6}-5z^{4}a^{-2}+17z^{4}a^{-4}-5z^{4}a^{-6}-6z^{2}a^{-2}+17z^{2}a^{-4}-7z^{2}a^{-6}-a^{-2}+5a^{-4}-3a^{-6}$

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

$z^{9}a^{-3}+z^{9}a^{-5}+2z^{8}a^{-2}+4z^{8}a^{-4}+2z^{8}a^{-6}+z^{7}a^{-1}-3z^{7}a^{-3}-2z^{7}a^{-5}+2z^{7}a^{-7}-11z^{6}a^{-2}-20z^{6}a^{-4}-7z^{6}a^{-6}+2z^{6}a^{-8}-5z^{5}a^{-1}-2z^{5}a^{-3}-3z^{5}a^{-5}-4z^{5}a^{-7}+2z^{5}a^{-9}+18z^{4}a^{-2}+32z^{4}a^{-4}+10z^{4}a^{-6}-2z^{4}a^{-8}+2z^{4}a^{-10}+6z^{3}a^{-1}+7z^{3}a^{-3}+6z^{3}a^{-5}+3z^{3}a^{-7}-z^{3}a^{-9}+z^{3}a^{-11}-10z^{2}a^{-2}-22z^{2}a^{-4}-9z^{2}a^{-6}+z^{2}a^{-8}-2z^{2}a^{-10}-za^{-1}-2za^{-3}-3za^{-5}-za^{-7}-za^{-11}+a^{-2}+5a^{-4}+3a^{-6}$

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, $q\leftrightarrow q^{-1}$): {}

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 5"];

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]=

{ $t^{4}-3t^{3}+5t^{2}-5t+5-5t^{-1}+5t^{-2}-3t^{-3}+t^{-4}$, $-q^{9}+2q^{8}-3q^{7}+4q^{6}-5q^{5}+5q^{4}-4q^{3}+4q^{2}-2q+2-q^{-1}$ }

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:

(4, 7)

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 $16$ $56$ $128$ ${\frac {728}{3}}$ ${\frac {16}{3}}$ $896$ ${\frac {3824}{3}}$ ${\frac {608}{3}}$ $24$ ${\frac {2048}{3}}$ $1568$ ${\frac {11648}{3}}$ ${\frac {256}{3}}$ ${\frac {104222}{15}}$ ${\frac {18512}{15}}$ ${\frac {38288}{45}}$ ${\frac {130}{9}}$ $-{\frac {658}{15}}$

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 $r$). The squares with yellow highlighting are those on the "critical diagonals", where $j-2r=s+1$ or $j-2r=s-1$, where $s=$4 is the signature of 10 5. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ -3 -2 -1 0 1 2 3 4 5 6 7 χ 19                     1 -1 17                   1   1 15                 2 1   -1 13               2 1     1 11             3 2       -1 9           2 2         0 7         2 3           1 5       2 2             0 3     1 3               2 1   1 1                 0 -1   1                   1 -3 1                     -1

Integral Khovanov Homology (db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$ $i=3$ $i=5$ $r=-3$ ${\mathbb {Z} }$ $r=-2$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=-1$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=0$ ${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }^{2}$ $r=1$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=2$ ${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=3$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{3}$ ${\mathbb {Z} }^{3}$ $r=4$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=5$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=6$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=7$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the $n+1$-dimensional representation of $sl(2)$)

$n$	$J_{n}$
2	$q^{25}-2q^{24}+4q^{22}-5q^{21}+7q^{19}-8q^{18}+q^{17}+8q^{16}-11q^{15}+3q^{14}+9q^{13}-13q^{12}+3q^{11}+11q^{10}-14q^{9}+q^{8}+13q^{7}-12q^{6}-q^{5}+13q^{4}-9q^{3}-3q^{2}+10q-4-4q^{-1}+5q^{-2}-q^{-3}-2q^{-4}+q^{-5}$
3	$-q^{48}+2q^{47}-q^{45}-3q^{44}+4q^{43}+3q^{42}-4q^{41}-7q^{40}+6q^{39}+10q^{38}-6q^{37}-14q^{36}+5q^{35}+18q^{34}-2q^{33}-22q^{32}-q^{31}+24q^{30}+5q^{29}-24q^{28}-9q^{27}+23q^{26}+11q^{25}-22q^{24}-10q^{23}+20q^{22}+7q^{21}-17q^{20}-6q^{19}+19q^{18}-2q^{17}-14q^{16}+18q^{14}-9q^{13}-11q^{12}+6q^{11}+16q^{10}-13q^{9}-11q^{8}+10q^{7}+17q^{6}-13q^{5}-14q^{4}+8q^{3}+18q^{2}-7q-15+2q^{-1}+14q^{-2}+q^{-3}-11q^{-4}-3q^{-5}+7q^{-6}+3q^{-7}-4q^{-8}-2q^{-9}+q^{-10}+2q^{-11}-q^{-12}$
4	$q^{78}-2q^{77}+q^{75}+4q^{73}-7q^{72}+q^{71}+2q^{70}+q^{69}+9q^{68}-18q^{67}+q^{66}+5q^{65}+8q^{64}+16q^{63}-36q^{62}-4q^{61}+8q^{60}+25q^{59}+29q^{58}-61q^{57}-19q^{56}+9q^{55}+52q^{54}+49q^{53}-88q^{52}-44q^{51}+4q^{50}+84q^{49}+77q^{48}-107q^{47}-71q^{46}-11q^{45}+104q^{44}+105q^{43}-108q^{42}-86q^{41}-30q^{40}+105q^{39}+118q^{38}-99q^{37}-82q^{36}-37q^{35}+91q^{34}+115q^{33}-89q^{32}-71q^{31}-35q^{30}+75q^{29}+108q^{28}-80q^{27}-58q^{26}-32q^{25}+54q^{24}+99q^{23}-66q^{22}-42q^{21}-29q^{20}+30q^{19}+85q^{18}-52q^{17}-23q^{16}-20q^{15}+11q^{14}+66q^{13}-43q^{12}-10q^{11}-9q^{10}+4q^{9}+51q^{8}-40q^{7}-8q^{6}-4q^{5}+6q^{4}+46q^{3}-34q^{2}-13q-9+5q^{-1}+45q^{-2}-19q^{-3}-12q^{-4}-16q^{-5}-4q^{-6}+35q^{-7}-3q^{-8}-4q^{-9}-14q^{-10}-10q^{-11}+18q^{-12}+2q^{-13}+2q^{-14}-5q^{-15}-7q^{-16}+5q^{-17}+q^{-18}+2q^{-19}-q^{-20}-2q^{-21}+q^{-22}$
5	$-q^{115}+2q^{114}-q^{112}-q^{110}-q^{109}+3q^{108}+q^{107}-3q^{106}+q^{105}-q^{104}+5q^{102}-q^{101}-7q^{100}-q^{99}+q^{98}+6q^{97}+11q^{96}-2q^{95}-18q^{94}-13q^{93}+3q^{92}+21q^{91}+26q^{90}-35q^{88}-37q^{87}+2q^{86}+45q^{85}+50q^{84}-3q^{83}-61q^{82}-63q^{81}+7q^{80}+83q^{79}+77q^{78}-17q^{77}-108q^{76}-92q^{75}+27q^{74}+137q^{73}+114q^{72}-37q^{71}-170q^{70}-138q^{69}+41q^{68}+199q^{67}+164q^{66}-37q^{65}-219q^{64}-192q^{63}+26q^{62}+233q^{61}+211q^{60}-15q^{59}-228q^{58}-224q^{57}-2q^{56}+224q^{55}+226q^{54}+12q^{53}-209q^{52}-224q^{51}-23q^{50}+198q^{49}+217q^{48}+33q^{47}-180q^{46}-220q^{45}-43q^{44}+173q^{43}+208q^{42}+58q^{41}-146q^{40}-221q^{39}-70q^{38}+139q^{37}+202q^{36}+90q^{35}-103q^{34}-211q^{33}-103q^{32}+90q^{31}+182q^{30}+117q^{29}-48q^{28}-179q^{27}-122q^{26}+31q^{25}+141q^{24}+124q^{23}+4q^{22}-124q^{21}-114q^{20}-16q^{19}+82q^{18}+104q^{17}+37q^{16}-66q^{15}-82q^{14}-33q^{13}+33q^{12}+66q^{11}+43q^{10}-30q^{9}-52q^{8}-25q^{7}+13q^{6}+40q^{5}+34q^{4}-18q^{3}-41q^{2}-22q+9+37q^{-1}+34q^{-2}-9q^{-3}-38q^{-4}-32q^{-5}-4q^{-6}+31q^{-7}+41q^{-8}+10q^{-9}-24q^{-10}-34q^{-11}-21q^{-12}+10q^{-13}+31q^{-14}+25q^{-15}-4q^{-16}-20q^{-17}-20q^{-18}-7q^{-19}+11q^{-20}+18q^{-21}+7q^{-22}-6q^{-23}-8q^{-24}-6q^{-25}-2q^{-26}+7q^{-27}+5q^{-28}-q^{-29}-2q^{-30}-q^{-31}-2q^{-32}+q^{-33}+2q^{-34}-q^{-35}$
6	$q^{159}-2q^{158}+q^{156}+q^{154}-2q^{153}+5q^{152}-5q^{151}+q^{149}-2q^{148}+2q^{147}-6q^{146}+13q^{145}-8q^{144}+5q^{143}+q^{142}-7q^{141}+q^{140}-16q^{139}+20q^{138}-11q^{137}+19q^{136}+7q^{135}-7q^{134}-q^{133}-39q^{132}+14q^{131}-24q^{130}+44q^{129}+27q^{128}+9q^{127}+10q^{126}-72q^{125}-12q^{124}-59q^{123}+62q^{122}+51q^{121}+42q^{120}+45q^{119}-89q^{118}-35q^{117}-110q^{116}+56q^{115}+42q^{114}+59q^{113}+94q^{112}-65q^{111}-6q^{110}-134q^{109}+32q^{108}-33q^{107}+5q^{106}+112q^{105}-7q^{104}+104q^{103}-76q^{102}+37q^{101}-150q^{100}-136q^{99}+46q^{98}+23q^{97}+247q^{96}+65q^{95}+125q^{94}-225q^{93}-291q^{92}-92q^{91}-35q^{90}+323q^{89}+203q^{88}+270q^{87}-201q^{86}-362q^{85}-209q^{84}-139q^{83}+295q^{82}+251q^{81}+372q^{80}-133q^{79}-334q^{78}-235q^{77}-200q^{76}+231q^{75}+216q^{74}+387q^{73}-87q^{72}-274q^{71}-203q^{70}-210q^{69}+180q^{68}+162q^{67}+365q^{66}-50q^{65}-214q^{64}-172q^{63}-225q^{62}+122q^{61}+107q^{60}+356q^{59}+22q^{58}-135q^{57}-153q^{56}-270q^{55}+32q^{54}+35q^{53}+353q^{52}+128q^{51}-20q^{50}-120q^{49}-323q^{48}-84q^{47}-66q^{46}+328q^{45}+233q^{44}+117q^{43}-53q^{42}-342q^{41}-191q^{40}-192q^{39}+252q^{38}+290q^{37}+242q^{36}+54q^{35}-290q^{34}-242q^{33}-310q^{32}+119q^{31}+257q^{30}+304q^{29}+167q^{28}-164q^{27}-196q^{26}-365q^{25}-25q^{24}+140q^{23}+265q^{22}+223q^{21}-24q^{20}-71q^{19}-319q^{18}-109q^{17}+12q^{16}+152q^{15}+186q^{14}+55q^{13}+52q^{12}-212q^{11}-103q^{10}-53q^{9}+50q^{8}+102q^{7}+57q^{6}+106q^{5}-127q^{4}-60q^{3}-54q^{2}+7q+45+40q^{-1}+109q^{-2}-89q^{-3}-41q^{-4}-51q^{-5}-7q^{-6}+22q^{-7}+43q^{-8}+113q^{-9}-57q^{-10}-32q^{-11}-60q^{-12}-32q^{-13}-8q^{-14}+36q^{-15}+115q^{-16}-11q^{-17}-4q^{-18}-47q^{-19}-44q^{-20}-42q^{-21}+3q^{-22}+83q^{-23}+15q^{-24}+24q^{-25}-14q^{-26}-24q^{-27}-44q^{-28}-21q^{-29}+37q^{-30}+8q^{-31}+23q^{-32}+6q^{-33}-q^{-34}-22q^{-35}-18q^{-36}+10q^{-37}-q^{-38}+9q^{-39}+5q^{-40}+5q^{-41}-7q^{-42}-7q^{-43}+3q^{-44}-2q^{-45}+2q^{-46}+q^{-47}+2q^{-48}-q^{-49}-2q^{-50}+q^{-51}$
7	$-q^{210}+2q^{209}-q^{207}-q^{205}+2q^{204}-2q^{203}-3q^{202}+4q^{201}+2q^{200}+q^{198}-3q^{197}+5q^{196}-4q^{195}-12q^{194}+4q^{193}+3q^{192}+5q^{191}+7q^{190}-2q^{189}+11q^{188}-5q^{187}-24q^{186}-6q^{185}-8q^{184}+7q^{183}+22q^{182}+11q^{181}+30q^{180}+6q^{179}-36q^{178}-30q^{177}-46q^{176}-18q^{175}+30q^{174}+43q^{173}+84q^{172}+52q^{171}-25q^{170}-56q^{169}-122q^{168}-104q^{167}-10q^{166}+68q^{165}+176q^{164}+167q^{163}+55q^{162}-50q^{161}-217q^{160}-264q^{159}-141q^{158}+22q^{157}+264q^{156}+359q^{155}+246q^{154}+51q^{153}-277q^{152}-469q^{151}-396q^{150}-165q^{149}+269q^{148}+580q^{147}+566q^{146}+321q^{145}-206q^{144}-663q^{143}-765q^{142}-543q^{141}+89q^{140}+723q^{139}+973q^{138}+798q^{137}+92q^{136}-725q^{135}-1155q^{134}-1087q^{133}-342q^{132}+656q^{131}+1304q^{130}+1377q^{129}+623q^{128}-520q^{127}-1371q^{126}-1616q^{125}-926q^{124}+315q^{123}+1360q^{122}+1790q^{121}+1198q^{120}-89q^{119}-1271q^{118}-1871q^{117}-1398q^{116}-129q^{115}+1129q^{114}+1860q^{113}+1520q^{112}+311q^{111}-985q^{110}-1803q^{109}-1556q^{108}-402q^{107}+862q^{106}+1699q^{105}+1528q^{104}+454q^{103}-782q^{102}-1624q^{101}-1473q^{100}-435q^{99}+750q^{98}+1550q^{97}+1398q^{96}+407q^{95}-728q^{94}-1497q^{93}-1349q^{92}-378q^{91}+728q^{90}+1454q^{89}+1277q^{88}+356q^{87}-685q^{86}-1388q^{85}-1236q^{84}-356q^{83}+647q^{82}+1310q^{81}+1150q^{80}+362q^{79}-552q^{78}-1196q^{77}-1085q^{76}-371q^{75}+467q^{74}+1060q^{73}+963q^{72}+380q^{71}-335q^{70}-900q^{69}-855q^{68}-372q^{67}+228q^{66}+719q^{65}+681q^{64}+354q^{63}-91q^{62}-523q^{61}-528q^{60}-301q^{59}+11q^{58}+325q^{57}+304q^{56}+215q^{55}+91q^{54}-140q^{53}-120q^{52}-99q^{51}-87q^{50}-9q^{49}-119q^{48}-59q^{47}+92q^{46}+119q^{45}+272q^{44}+215q^{43}+17q^{42}-145q^{41}-430q^{40}-395q^{39}-109q^{38}+120q^{37}+478q^{36}+506q^{35}+271q^{34}-13q^{33}-480q^{32}-594q^{31}-382q^{30}-115q^{29}+383q^{28}+585q^{27}+483q^{26}+260q^{25}-255q^{24}-518q^{23}-490q^{22}-382q^{21}+89q^{20}+393q^{19}+466q^{18}+433q^{17}+39q^{16}-235q^{15}-347q^{14}-447q^{13}-153q^{12}+104q^{11}+243q^{10}+383q^{9}+179q^{8}+12q^{7}-101q^{6}-314q^{5}-192q^{4}-64q^{3}+24q^{2}+220q+151+93q^{-1}+47q^{-2}-162q^{-3}-124q^{-4}-85q^{-5}-74q^{-6}+106q^{-7}+97q^{-8}+91q^{-9}+93q^{-10}-85q^{-11}-82q^{-12}-80q^{-13}-109q^{-14}+44q^{-15}+66q^{-16}+95q^{-17}+128q^{-18}-20q^{-19}-51q^{-20}-78q^{-21}-135q^{-22}-26q^{-23}+12q^{-24}+68q^{-25}+144q^{-26}+49q^{-27}+12q^{-28}-35q^{-29}-115q^{-30}-63q^{-31}-50q^{-32}-q^{-33}+92q^{-34}+67q^{-35}+52q^{-36}+21q^{-37}-52q^{-38}-39q^{-39}-54q^{-40}-44q^{-41}+25q^{-42}+29q^{-43}+42q^{-44}+33q^{-45}-9q^{-46}-5q^{-47}-20q^{-48}-33q^{-49}-6q^{-50}+2q^{-51}+16q^{-52}+19q^{-53}-2q^{-54}+4q^{-55}-q^{-56}-11q^{-57}-5q^{-58}-4q^{-59}+4q^{-60}+7q^{-61}-q^{-62}+2q^{-64}-2q^{-65}-q^{-66}-2q^{-67}+q^{-68}+2q^{-69}-q^{-70}$

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.

10_4 10_6