10 142

10_141

10_143

(KnotPlot image)	See the full Rolfsen Knot Table. Visit 10 142's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 142 at Knotilus!
	10_142 is also known as the pretzel knot P(-4,3,3).

Knot presentations

Planar diagram presentation	X4251 X10,4,11,3 X11,19,12,18 X5,15,6,14 X17,7,18,6 X7,17,8,16 X15,9,16,8 X13,1,14,20 X19,13,20,12 X2,10,3,9
Gauss code	1, -10, 2, -1, -4, 5, -6, 7, 10, -2, -3, 9, -8, 4, -7, 6, -5, 3, -9, 8
Dowker-Thistlethwaite code	4 10 -14 -16 2 -18 -20 -8 -6 -12
Conway Notation	[31,3,3-]

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

[edit Notes on presentations of 10 142]

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["10 142"];

In[4]:=

PD[K]

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

Out[4]=

X4251 X10,4,11,3 X11,19,12,18 X5,15,6,14 X17,7,18,6 X7,17,8,16 X15,9,16,8 X13,1,14,20 X19,13,20,12 X2,10,3,9

In[5]:=

GaussCode[K]

Out[5]=

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

In[6]:=

DTCode[K]

Out[6]=

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

(The path below may be different on your system)

In[7]:=

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

In[8]:=

ConwayNotation[K]

Out[8]=

[31,3,3-]

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]=

${\textrm {BR}}(4,\{1,1,1,2,1,1,1,2,3,-2,3\})$

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]=

{ 4, 11, 4 }

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

In[14]:=

Draw[ap]

Out[14]=

-Graphics-

Three dimensional invariants

Symmetry type Reversible Unknotting number 3 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 2 Maximal Thurston-Bennequin number [5][-14] Hyperbolic Volume 6.77082 A-Polynomial See Data:10 142/A-polynomial

[edit Notes for 10 142's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus $3$ Topological 4 genus $3$ Concordance genus $3$ Rasmussen s-Invariant -6

[edit Notes for 10 142's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$2t^{3}-3t^{2}+2t-1+2t^{-1}-3t^{-2}+2t^{-3}$
Conway polynomial	$2z^{6}+9z^{4}+8z^{2}+1$
2nd Alexander ideal (db, data sources)	$\left\{2,t^{2}+t+1\right\}$
Determinant and Signature	{ 15, 6 }
Jones polynomial	$-2q^{10}+2q^{9}-2q^{8}+3q^{7}-2q^{6}+2q^{5}-q^{4}+q^{3}$
HOMFLY-PT polynomial (db, data sources)	$z^{6}a^{-6}+z^{6}a^{-8}+5z^{4}a^{-6}+5z^{4}a^{-8}-z^{4}a^{-10}+6z^{2}a^{-6}+7z^{2}a^{-8}-5z^{2}a^{-10}+a^{-6}+4a^{-8}-5a^{-10}+a^{-12}$
Kauffman polynomial (db, data sources)	$z^{8}a^{-8}+z^{8}a^{-10}+z^{7}a^{-7}+2z^{7}a^{-9}+z^{7}a^{-11}+z^{6}a^{-6}-5z^{6}a^{-8}-6z^{6}a^{-10}-4z^{5}a^{-7}-9z^{5}a^{-9}-5z^{5}a^{-11}-5z^{4}a^{-6}+9z^{4}a^{-8}+15z^{4}a^{-10}+z^{4}a^{-12}+3z^{3}a^{-7}+12z^{3}a^{-9}+9z^{3}a^{-11}+6z^{2}a^{-6}-10z^{2}a^{-8}-17z^{2}a^{-10}-z^{2}a^{-12}-6za^{-9}-4za^{-11}+2za^{-13}-a^{-6}+4a^{-8}+5a^{-10}+a^{-12}$
The A2 invariant	$q^{-10}+q^{-14}+q^{-18}+q^{-20}+2q^{-22}+3q^{-24}-q^{-28}-3q^{-30}-2q^{-32}-q^{-34}+q^{-38}$
The G2 invariant	$q^{-50}+q^{-54}-q^{-56}+q^{-58}+3q^{-64}-2q^{-66}+4q^{-68}-q^{-70}-q^{-72}+3q^{-74}-2q^{-76}+2q^{-78}-q^{-82}+3q^{-84}+3q^{-90}-4q^{-92}+4q^{-94}-2q^{-98}+5q^{-100}-2q^{-102}+4q^{-104}+q^{-106}+3q^{-108}+2q^{-110}-2q^{-112}+q^{-114}+3q^{-118}-q^{-120}-3q^{-122}-q^{-124}+q^{-126}-q^{-130}-9q^{-132}+q^{-136}-4q^{-138}-7q^{-142}+q^{-144}+3q^{-146}-3q^{-148}-2q^{-150}-2q^{-152}+q^{-154}+3q^{-156}-q^{-158}-q^{-160}+2q^{-162}+2q^{-166}+2q^{-168}-q^{-170}+q^{-172}$

Further Quantum Invariants

Further quantum knot invariants for 10_142.

A1 Invariants.

Weight	Invariant
1	$q^{-5}+q^{-9}+q^{-13}+q^{-15}-2q^{-21}$
2	$q^{-10}+2q^{-16}+q^{-18}-q^{-20}+q^{-22}+2q^{-24}-q^{-28}-q^{-34}+q^{-36}+2q^{-38}-q^{-40}-q^{-46}-3q^{-48}-q^{-50}-q^{-54}+q^{-56}+q^{-58}+q^{-60}$
3	$q^{-15}+q^{-21}+2q^{-23}+q^{-25}-q^{-27}-q^{-29}+2q^{-31}+3q^{-33}+q^{-35}-2q^{-37}-2q^{-39}+q^{-41}+3q^{-43}+q^{-45}-2q^{-47}-3q^{-49}+q^{-51}+4q^{-53}+q^{-55}-4q^{-57}-3q^{-59}+2q^{-61}+2q^{-63}-3q^{-65}-2q^{-67}+3q^{-69}+q^{-71}-2q^{-73}-q^{-75}+q^{-77}-q^{-81}-3q^{-83}-2q^{-85}+3q^{-89}-2q^{-91}-4q^{-93}+7q^{-97}+4q^{-99}-2q^{-101}-2q^{-103}+q^{-105}+4q^{-107}-2q^{-111}-2q^{-113}$

A2 Invariants.

Weight	Invariant
1,0	$q^{-10}+q^{-14}+q^{-18}+q^{-20}+2q^{-22}+3q^{-24}-q^{-28}-3q^{-30}-2q^{-32}-q^{-34}+q^{-38}$
1,1	$q^{-20}+2q^{-24}-2q^{-26}+6q^{-28}-2q^{-30}+12q^{-32}-2q^{-34}+7q^{-36}+6q^{-42}-10q^{-44}+10q^{-46}-10q^{-48}+8q^{-50}-11q^{-52}+2q^{-54}-8q^{-56}-4q^{-58}-3q^{-60}-6q^{-62}+6q^{-64}-4q^{-66}+10q^{-68}+2q^{-72}+2q^{-74}-2q^{-76}-2q^{-78}-4q^{-80}-2q^{-82}+4q^{-84}+2q^{-88}$
2,0	$q^{-20}+q^{-26}+2q^{-28}+q^{-30}+q^{-32}+2q^{-34}+3q^{-36}+2q^{-38}+q^{-40}+q^{-42}-q^{-46}+q^{-52}+2q^{-54}+3q^{-56}+2q^{-58}+q^{-60}-4q^{-62}-6q^{-64}-10q^{-66}-9q^{-68}-5q^{-70}-q^{-72}+3q^{-74}+4q^{-76}+6q^{-78}+5q^{-80}+4q^{-82}-2q^{-88}-2q^{-90}-q^{-92}+q^{-96}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{-20}+q^{-24}+q^{-26}+q^{-30}+2q^{-32}+3q^{-34}+5q^{-36}+4q^{-38}+4q^{-40}+2q^{-42}-3q^{-46}-3q^{-48}-5q^{-50}-4q^{-52}-4q^{-54}-3q^{-56}-q^{-58}-q^{-60}+q^{-62}+q^{-64}+q^{-66}+q^{-68}+2q^{-70}$
1,0,0	$q^{-15}+q^{-19}+q^{-23}+2q^{-27}+3q^{-29}+3q^{-31}+3q^{-33}-q^{-37}-4q^{-39}-3q^{-41}-3q^{-43}-q^{-45}+q^{-49}+q^{-51}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{-30}+q^{-34}+q^{-36}+q^{-38}+2q^{-42}+2q^{-44}+4q^{-46}+5q^{-48}+5q^{-50}+7q^{-52}+7q^{-54}+5q^{-56}+4q^{-58}+4q^{-60}+2q^{-62}-2q^{-64}-4q^{-66}-6q^{-68}-10q^{-70}-14q^{-72}-12q^{-74}-12q^{-76}-10q^{-78}-2q^{-80}+3q^{-82}+6q^{-84}+8q^{-86}+10q^{-88}+6q^{-90}+2q^{-92}-2q^{-98}-2q^{-100}$
1,0,0,0	$q^{-20}+q^{-24}+q^{-28}+q^{-32}+2q^{-34}+3q^{-36}+4q^{-38}+3q^{-40}+3q^{-42}-q^{-46}-4q^{-48}-4q^{-50}-4q^{-52}-3q^{-54}-q^{-56}+q^{-60}+q^{-62}+q^{-64}$

B2 Invariants.

Weight	Invariant
0,1	$q^{-20}+q^{-24}-q^{-26}+2q^{-28}-q^{-30}+2q^{-32}+q^{-34}+q^{-36}+2q^{-38}+2q^{-42}-2q^{-44}+3q^{-46}-3q^{-48}+q^{-50}-2q^{-52}-q^{-56}-q^{-58}+q^{-60}-q^{-62}+q^{-64}-q^{-66}+q^{-68}-2q^{-70}$
1,0	$q^{-30}+q^{-38}+q^{-40}-q^{-44}+q^{-46}+2q^{-48}+q^{-50}-q^{-52}+2q^{-54}+3q^{-56}+3q^{-58}+q^{-60}+q^{-62}+q^{-64}+2q^{-66}-q^{-70}-q^{-72}-q^{-76}-2q^{-78}-2q^{-80}-q^{-82}-2q^{-86}-3q^{-88}-2q^{-90}-q^{-94}-2q^{-96}-q^{-98}+q^{-100}+q^{-102}+q^{-108}+q^{-110}+2q^{-112}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{-30}+q^{-34}+2q^{-38}-q^{-40}+2q^{-42}+3q^{-46}+3q^{-48}+3q^{-50}+5q^{-52}+5q^{-54}+6q^{-56}+3q^{-58}+4q^{-60}-2q^{-62}-6q^{-66}-4q^{-68}-8q^{-70}-5q^{-72}-6q^{-74}-3q^{-76}-2q^{-78}-q^{-80}+q^{-82}+2q^{-86}+2q^{-90}+q^{-94}+2q^{-98}$

G2 Invariants.

Weight

Invariant

1,0

$q^{-50}+q^{-54}-q^{-56}+q^{-58}+3q^{-64}-2q^{-66}+4q^{-68}-q^{-70}-q^{-72}+3q^{-74}-2q^{-76}+2q^{-78}-q^{-82}+3q^{-84}+3q^{-90}-4q^{-92}+4q^{-94}-2q^{-98}+5q^{-100}-2q^{-102}+4q^{-104}+q^{-106}+3q^{-108}+2q^{-110}-2q^{-112}+q^{-114}+3q^{-118}-q^{-120}-3q^{-122}-q^{-124}+q^{-126}-q^{-130}-9q^{-132}+q^{-136}-4q^{-138}-7q^{-142}+q^{-144}+3q^{-146}-3q^{-148}-2q^{-150}-2q^{-152}+q^{-154}+3q^{-156}-q^{-158}-q^{-160}+2q^{-162}+2q^{-166}+2q^{-168}-q^{-170}+q^{-172}$

.

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["10 142"];

In[4]:=

Alexander[K][t]

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

Out[4]=

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

In[5]:=

Conway[K][z]

Out[5]=

$2z^{6}+9z^{4}+8z^{2}+1$

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]=

$\left\{2,t^{2}+t+1\right\}$

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 15, 6 }

In[8]:=

Jones[K][q]

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

Out[8]=

$-2q^{10}+2q^{9}-2q^{8}+3q^{7}-2q^{6}+2q^{5}-q^{4}+q^{3}$

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

$z^{6}a^{-6}+z^{6}a^{-8}+5z^{4}a^{-6}+5z^{4}a^{-8}-z^{4}a^{-10}+6z^{2}a^{-6}+7z^{2}a^{-8}-5z^{2}a^{-10}+a^{-6}+4a^{-8}-5a^{-10}+a^{-12}$

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

$z^{8}a^{-8}+z^{8}a^{-10}+z^{7}a^{-7}+2z^{7}a^{-9}+z^{7}a^{-11}+z^{6}a^{-6}-5z^{6}a^{-8}-6z^{6}a^{-10}-4z^{5}a^{-7}-9z^{5}a^{-9}-5z^{5}a^{-11}-5z^{4}a^{-6}+9z^{4}a^{-8}+15z^{4}a^{-10}+z^{4}a^{-12}+3z^{3}a^{-7}+12z^{3}a^{-9}+9z^{3}a^{-11}+6z^{2}a^{-6}-10z^{2}a^{-8}-17z^{2}a^{-10}-z^{2}a^{-12}-6za^{-9}-4za^{-11}+2za^{-13}-a^{-6}+4a^{-8}+5a^{-10}+a^{-12}$

"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["10 142"];

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]=

{ $2t^{3}-3t^{2}+2t-1+2t^{-1}-3t^{-2}+2t^{-3}$, $-2q^{10}+2q^{9}-2q^{8}+3q^{7}-2q^{6}+2q^{5}-q^{4}+q^{3}$ }

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:

(8, 21)

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 $32$ $168$ $512$ ${\frac {3520}{3}}$ ${\frac {536}{3}}$ $5376$ $9072$ $1600$ $1160$ ${\frac {16384}{3}}$ $14112$ ${\frac {112640}{3}}$ ${\frac {17152}{3}}$ ${\frac {1074964}{15}}$ ${\frac {12488}{5}}$ ${\frac {1215256}{45}}$ ${\frac {3644}{9}}$ ${\frac {52564}{15}}$

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=$6 is the signature of 10 142. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ 0 1 2 3 4 5 6 7 χ 21               2 -2 19                 0 17           2 2   0 15         1       1 13       1 2       1 11     1 1         0 9     1           1 7 1 1             0 5 1               1

Integral Khovanov Homology (db, data source)

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

The Coloured Jones Polynomials

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

$n$	$J_{n}$
2	$q^{29}-q^{26}+q^{25}-q^{24}-3q^{23}+3q^{22}-3q^{20}+2q^{19}+3q^{18}-4q^{17}+4q^{15}-4q^{14}-q^{13}+5q^{12}-2q^{11}-2q^{10}+3q^{9}-q^{7}+q^{6}$
3	$-2q^{55}+2q^{53}+4q^{52}-5q^{51}-3q^{50}+2q^{49}+10q^{48}-2q^{47}-10q^{46}-2q^{45}+12q^{44}+3q^{43}-13q^{42}-4q^{41}+11q^{40}+5q^{39}-12q^{38}-3q^{37}+9q^{36}+4q^{35}-9q^{34}-q^{33}+4q^{32}+3q^{31}-4q^{30}-q^{29}-q^{28}+2q^{27}+q^{26}+2q^{25}-4q^{24}-2q^{23}+2q^{22}+5q^{21}-2q^{20}-4q^{19}-q^{18}+5q^{17}+q^{16}-2q^{15}-2q^{14}+2q^{13}+q^{12}-q^{10}+q^{9}$
4	$q^{90}+2q^{88}-2q^{87}-4q^{86}-q^{85}-q^{84}+10q^{83}+5q^{82}-9q^{81}-11q^{80}-11q^{79}+19q^{78}+23q^{77}-4q^{76}-20q^{75}-30q^{74}+19q^{73}+36q^{72}+8q^{71}-22q^{70}-42q^{69}+12q^{68}+39q^{67}+15q^{66}-19q^{65}-45q^{64}+9q^{63}+37q^{62}+13q^{61}-14q^{60}-41q^{59}+6q^{58}+34q^{57}+12q^{56}-9q^{55}-36q^{54}-q^{53}+29q^{52}+11q^{51}-q^{50}-28q^{49}-10q^{48}+18q^{47}+9q^{46}+9q^{45}-14q^{44}-13q^{43}+6q^{42}+q^{41}+12q^{40}-q^{39}-8q^{38}+2q^{37}-8q^{36}+5q^{35}+3q^{34}+7q^{32}-9q^{31}-q^{30}-2q^{29}-q^{28}+10q^{27}-2q^{26}-4q^{24}-4q^{23}+6q^{22}+2q^{20}-q^{19}-3q^{18}+2q^{17}+q^{15}-q^{13}+q^{12}$
5	$-2q^{132}+2q^{129}+2q^{128}+4q^{127}-q^{126}-3q^{125}-7q^{124}-5q^{123}+2q^{122}+10q^{121}+14q^{120}+10q^{119}-13q^{118}-27q^{117}-23q^{116}+37q^{114}+48q^{113}+11q^{112}-45q^{111}-63q^{110}-33q^{109}+41q^{108}+83q^{107}+51q^{106}-37q^{105}-89q^{104}-64q^{103}+26q^{102}+92q^{101}+74q^{100}-19q^{99}-90q^{98}-76q^{97}+15q^{96}+86q^{95}+75q^{94}-12q^{93}-85q^{92}-71q^{91}+11q^{90}+81q^{89}+71q^{88}-12q^{87}-79q^{86}-65q^{85}+8q^{84}+72q^{83}+66q^{82}-2q^{81}-66q^{80}-63q^{79}-5q^{78}+53q^{77}+63q^{76}+17q^{75}-44q^{74}-59q^{73}-24q^{72}+24q^{71}+53q^{70}+36q^{69}-13q^{68}-42q^{67}-36q^{66}-6q^{65}+27q^{64}+38q^{63}+16q^{62}-13q^{61}-27q^{60}-24q^{59}-3q^{58}+17q^{57}+20q^{56}+14q^{55}-4q^{54}-15q^{53}-14q^{52}-5q^{51}+2q^{50}+12q^{49}+9q^{48}+3q^{47}-3q^{46}-5q^{45}-8q^{44}-3q^{43}+q^{42}+5q^{41}+4q^{40}+5q^{39}-q^{38}-3q^{37}-5q^{36}-4q^{35}+5q^{33}+3q^{32}+3q^{31}-q^{30}-4q^{29}-3q^{28}+2q^{27}+2q^{25}+2q^{24}-q^{23}-2q^{22}+q^{21}+q^{18}-q^{16}+q^{15}$
6	$q^{183}+2q^{181}-2q^{179}-4q^{178}-4q^{177}-3q^{176}+q^{175}+10q^{174}+9q^{173}+8q^{172}-q^{171}-7q^{170}-25q^{169}-23q^{168}-q^{167}+14q^{166}+37q^{165}+38q^{164}+33q^{163}-28q^{162}-65q^{161}-63q^{160}-45q^{159}+27q^{158}+88q^{157}+136q^{156}+42q^{155}-58q^{154}-131q^{153}-156q^{152}-60q^{151}+83q^{150}+227q^{149}+151q^{148}+16q^{147}-138q^{146}-234q^{145}-161q^{144}+27q^{143}+247q^{142}+211q^{141}+87q^{140}-101q^{139}-245q^{138}-204q^{137}-20q^{136}+228q^{135}+215q^{134}+111q^{133}-76q^{132}-230q^{131}-205q^{130}-29q^{129}+216q^{128}+203q^{127}+106q^{126}-73q^{125}-220q^{124}-197q^{123}-25q^{122}+211q^{121}+192q^{120}+103q^{119}-68q^{118}-208q^{117}-190q^{116}-33q^{115}+193q^{114}+178q^{113}+110q^{112}-43q^{111}-180q^{110}-182q^{109}-60q^{108}+145q^{107}+154q^{106}+126q^{105}+5q^{104}-129q^{103}-167q^{102}-100q^{101}+70q^{100}+110q^{99}+135q^{98}+65q^{97}-52q^{96}-127q^{95}-126q^{94}-12q^{93}+37q^{92}+110q^{91}+102q^{90}+30q^{89}-50q^{88}-104q^{87}-62q^{86}-41q^{85}+38q^{84}+80q^{83}+69q^{82}+28q^{81}-32q^{80}-43q^{79}-68q^{78}-29q^{77}+12q^{76}+37q^{75}+49q^{74}+23q^{73}+14q^{72}-29q^{71}-33q^{70}-28q^{69}-16q^{68}+14q^{67}+14q^{66}+32q^{65}+13q^{64}+4q^{63}-11q^{62}-22q^{61}-8q^{60}-17q^{59}+7q^{58}+8q^{57}+15q^{56}+8q^{55}+6q^{53}-16q^{52}-4q^{51}-7q^{50}+q^{49}-q^{48}+2q^{47}+14q^{46}-3q^{45}+4q^{44}-3q^{43}-q^{42}-8q^{41}-5q^{40}+7q^{39}-2q^{38}+5q^{37}+2q^{36}+3q^{35}-4q^{34}-4q^{33}+3q^{32}-3q^{31}+q^{30}+q^{29}+3q^{28}-q^{27}-2q^{26}+2q^{25}-q^{24}+q^{21}-q^{19}+q^{18}$
7	${\textrm {NotAvailable}}(q)$

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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