12n
0648
(K12n
0648
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 8 11 2 5 3 4 6 9
Solving Sequence
3,9
10 4
5,11
8 6 2 1 7 12
c
9
c
3
c
10
c
8
c
5
c
2
c
1
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.95358 × 10
37
u
23
− 4.07407 × 10
36
u
22
+ ··· + 1.61095 × 10
39
b − 9.52256 × 10
39
,
− 7.06431 × 10
39
u
23
+ 8.51893 × 10
38
u
22
+ ··· + 2.30366 × 10
41
a − 7.64291 × 10
41
,
u
24
+ u
23
+ ··· + 289u + 143i
I
u
2
= h−u
18
− u
17
+ ··· + b − 1, −2u
16
− u
15
+ ··· + a − 1, u
19
− 12u
17
+ ··· + 4u − 1i
* 2 irreducible components of dim
C
= 0, with total 43 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−6.95 × 10
37
u
23
− 4.07 × 10
36
u
22
+ · · · + 1.61 × 10
39
b − 9.52 ×
10
39
, −7.06 × 10
39
u
23
+ 8.52 × 10
38
u
22
+ · · · + 2.30 × 10
41
a − 7.64 ×
10
41
, u
24
+ u
23
+ · · · + 289u + 143i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
5
=
0.0306656u
23
− 0.00369799u
22
+ ··· + 2.32158u + 3.31772
0.0431644u
23
+ 0.00252898u
22
+ ··· + 7.19118u + 5.91114
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
0.0142787u
23
− 0.00544253u
22
+ ··· + 2.94433u + 2.42345
0.0139246u
23
− 0.0131718u
22
+ ··· + 1.01894u + 0.464061
a
6
=
0.0251613u
23
− 0.000730907u
22
+ ··· + 1.76692u + 2.55543
−0.0181599u
23
+ 0.00533470u
22
+ ··· − 1.56432u − 1.98558
a
2
=
−0.0497304u
23
+ 0.00323432u
22
+ ··· − 6.95114u − 7.14443
−0.0419268u
23
− 0.00473941u
22
+ ··· − 4.93122u − 6.22408
a
1
=
−0.0497304u
23
+ 0.00323432u
22
+ ··· − 6.95114u − 7.14443
0.0148906u
23
− 0.00607853u
22
+ ··· + 3.26414u + 1.34988
a
7
=
−0.0265932u
23
− 0.00297561u
22
+ ··· − 2.70453u − 3.73203
0.00559528u
23
− 0.00695287u
22
+ ··· + 0.504854u + 0.119250
a
12
=
−0.0348398u
23
− 0.00284421u
22
+ ··· − 3.68700u − 5.79455
0.0148906u
23
− 0.00607853u
22
+ ··· + 3.26414u + 1.34988
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0449908u
23
+ 0.00298260u
22
+ ··· − 19.5117u − 16.1952
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 60u
23
+ ··· + 3708160u + 295936
c
2
, c
7
u
24
− 10u
23
+ ··· + 16u + 544
c
3
, c
9
, c
10
u
24
− u
23
+ ··· − 289u + 143
c
4
u
24
+ 3u
23
+ ··· − 327u − 41
c
5
, c
8
u
24
+ 2u
23
+ ··· + 13u − 1
c
6
, c
11
u
24
− u
23
+ ··· − 288u − 69
c
12
u
24
− 36u
22
+ ··· − 47638u − 14543
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 296y
23
+ ··· − 4939910283264y + 87578116096
c
2
, c
7
y
24
− 60y
23
+ ··· − 3708160y + 295936
c
3
, c
9
, c
10
y
24
− 45y
23
+ ··· − 70079y + 20449
c
4
y
24
− 11y
23
+ ··· − 33785y + 1681
c
5
, c
8
y
24
+ 26y
23
+ ··· − 575y + 1
c
6
, c
11
y
24
− 9y
23
+ ··· − 35058y + 4761
c
12
y
24
− 72y
23
+ ··· − 2969653580y + 211498849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.998180 + 0.182421I
a = −0.371865 + 0.963824I
b = −0.46248 + 1.36040I
−2.89773 − 4.47411I −11.26620 + 4.32225I
u = −0.998180 − 0.182421I
a = −0.371865 − 0.963824I
b = −0.46248 − 1.36040I
−2.89773 + 4.47411I −11.26620 − 4.32225I
u = −1.08785
a = 0.370138
b = 0.466022
−5.81657 −15.7030
u = −0.908883 + 0.696346I
a = 0.819047 − 0.748643I
b = −1.50457 − 0.48587I
2.29616 + 2.53148I −13.0553 − 13.0894I
u = −0.908883 − 0.696346I
a = 0.819047 + 0.748643I
b = −1.50457 + 0.48587I
2.29616 − 2.53148I −13.0553 + 13.0894I
u = −0.369638 + 0.655856I
a = 0.163913 + 0.088570I
b = −0.483150 + 1.254690I
−1.35028 − 2.85129I −8.82275 − 0.17568I
u = −0.369638 − 0.655856I
a = 0.163913 − 0.088570I
b = −0.483150 − 1.254690I
−1.35028 + 2.85129I −8.82275 + 0.17568I
u = 0.351833 + 0.653611I
a = −1.42495 − 0.28417I
b = 0.440762 − 1.267520I
−3.72902 − 2.23669I −11.06844 + 3.08943I
u = 0.351833 − 0.653611I
a = −1.42495 + 0.28417I
b = 0.440762 + 1.267520I
−3.72902 + 2.23669I −11.06844 − 3.08943I
u = 1.312160 + 0.113933I
a = −0.648596 + 1.219050I
b = 0.265262 + 0.114333I
−2.00982 − 3.68666I −7.35603 + 5.27682I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.312160 − 0.113933I
a = −0.648596 − 1.219050I
b = 0.265262 − 0.114333I
−2.00982 + 3.68666I −7.35603 − 5.27682I
u = −1.42954 + 0.07398I
a = −0.35156 − 1.37276I
b = 0.443663 − 1.115380I
−9.16253 − 3.52152I −17.4723 + 4.9311I
u = −1.42954 − 0.07398I
a = −0.35156 + 1.37276I
b = 0.443663 + 1.115380I
−9.16253 + 3.52152I −17.4723 − 4.9311I
u = −0.172334 + 0.521929I
a = 0.57148 − 1.66997I
b = −0.572916 + 0.049432I
2.32011 + 1.43982I −3.19830 − 4.08238I
u = −0.172334 − 0.521929I
a = 0.57148 + 1.66997I
b = −0.572916 − 0.049432I
2.32011 − 1.43982I −3.19830 + 4.08238I
u = 0.406773
a = −0.663948
b = 0.198801
−0.603529 −16.4560
u = 1.77917
a = 0.251024
b = −0.0435926
−16.2026 −29.6210
u = −2.04114 + 0.56230I
a = −0.502493 + 0.953370I
b = 1.10365 + 1.70631I
14.2564 + 11.7505I −11.51618 − 4.21495I
u = −2.04114 − 0.56230I
a = −0.502493 − 0.953370I
b = 1.10365 − 1.70631I
14.2564 − 11.7505I −11.51618 + 4.21495I
u = 2.37547 + 0.30331I
a = 0.174548 + 1.000270I
b = −0.11023 + 2.21127I
14.5489 − 0.5683I −8.00000 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.37547 − 0.30331I
a = 0.174548 − 1.000270I
b = −0.11023 − 2.21127I
14.5489 + 0.5683I −8.00000 + 0.I
u = 2.14046 + 1.17450I
a = −0.469141 − 0.647096I
b = 0.27079 − 2.64157I
−13.27670 − 2.35671I 0
u = 2.14046 − 1.17450I
a = −0.469141 + 0.647096I
b = 0.27079 + 2.64157I
−13.27670 + 2.35671I 0
u = −2.61851
a = 0.128998
b = 2.59719
18.9868 −8.00000
7
II.
I
u
2
= h−u
18
−u
17
+· · ·+b−1, −2u
16
−u
15
+· · ·+a−1, u
19
−12u
17
+· · ·+4u−1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
5
=
2u
16
+ u
15
+ ··· + 6u + 1
u
18
+ u
17
+ ··· − u + 1
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
−u
18
− u
17
+ ··· + 17u
3
− 7u
2
u
17
+ u
16
+ ··· + u − 1
a
6
=
u
17
+ 2u
16
+ ··· − 10u
2
+ 2u
u
16
− 10u
14
+ ··· + u − 1
a
2
=
u
18
− 12u
16
+ ··· − 8u + 2
u
18
+ 2u
17
+ ··· − 7u + 2
a
1
=
u
18
− 12u
16
+ ··· − 8u + 2
u
18
+ 2u
17
+ ··· − 8u + 2
a
7
=
−u
18
+ 12u
16
+ ··· + 5u − 1
u
18
+ u
17
+ ··· + 2u
2
− 2u
a
12
=
2u
18
+ 2u
17
+ ··· − 16u + 4
u
18
+ 2u
17
+ ··· − 8u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
18
−7u
17
+ 4u
16
+ 70u
15
+ 15u
14
−288u
13
−116u
12
+ 648u
11
+
286u
10
− 880u
9
− 387u
8
+ 725u
7
+ 321u
6
− 320u
5
− 125u
4
+ 53u
3
− 15u
2
− 11u − 7
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 16u
18
+ ··· + 9u − 1
c
2
u
19
− 8u
17
+ ··· + u + 1
c
3
u
19
− 12u
17
+ ··· + 4u + 1
c
4
u
19
− 2u
18
+ ··· + 5u
2
+ 1
c
5
u
19
+ 3u
18
+ ··· − 6u
2
− 1
c
6
u
19
+ 2u
17
+ ··· − u − 1
c
7
u
19
− 8u
17
+ ··· + u − 1
c
8
u
19
− 3u
18
+ ··· + 6u
2
+ 1
c
9
, c
10
u
19
− 12u
17
+ ··· + 4u − 1
c
11
u
19
+ 2u
17
+ ··· − u + 1
c
12
u
19
− u
18
+ ··· − 39u − 169
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 32y
18
+ ··· − 19y −1
c
2
, c
7
y
19
− 16y
18
+ ··· + 9y −1
c
3
, c
9
, c
10
y
19
− 24y
18
+ ··· − 4y
2
− 1
c
4
y
19
+ 6y
18
+ ··· − 10y −1
c
5
, c
8
y
19
+ 7y
18
+ ··· − 12y −1
c
6
, c
11
y
19
+ 4y
18
+ ··· − 13y −1
c
12
y
19
− 7y
18
+ ··· − 20111y −28561
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.980950 + 0.604076I
a = −0.798772 − 0.755373I
b = 1.49647 − 0.52355I
2.48141 − 2.27470I 1.66056 − 6.57716I
u = 0.980950 − 0.604076I
a = −0.798772 + 0.755373I
b = 1.49647 + 0.52355I
2.48141 + 2.27470I 1.66056 + 6.57716I
u = −0.737628 + 0.359811I
a = 0.067452 − 0.920420I
b = −0.762089 + 0.832433I
−5.41374 − 1.59276I −15.0492 + 2.8168I
u = −0.737628 − 0.359811I
a = 0.067452 + 0.920420I
b = −0.762089 − 0.832433I
−5.41374 + 1.59276I −15.0492 − 2.8168I
u = −1.179440 + 0.170240I
a = 0.90264 − 1.49402I
b = −0.490604 − 1.115980I
−7.08654 + 3.52788I −12.56931 − 3.15212I
u = −1.179440 − 0.170240I
a = 0.90264 + 1.49402I
b = −0.490604 + 1.115980I
−7.08654 − 3.52788I −12.56931 + 3.15212I
u = 1.277010 + 0.114842I
a = −0.193294 − 0.314119I
b = 0.305041 − 1.145700I
−4.51476 − 5.17759I −14.4043 + 6.7554I
u = 1.277010 − 0.114842I
a = −0.193294 + 0.314119I
b = 0.305041 + 1.145700I
−4.51476 + 5.17759I −14.4043 − 6.7554I
u = 1.340980 + 0.147089I
a = −0.55132 + 2.05499I
b = 0.135134 + 0.767547I
−2.81013 − 3.35015I −16.3799 + 1.5970I
u = 1.340980 − 0.147089I
a = −0.55132 − 2.05499I
b = 0.135134 − 0.767547I
−2.81013 + 3.35015I −16.3799 − 1.5970I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42878 + 0.22236I
a = 0.635513 + 0.360503I
b = −0.044798 + 0.642597I
−3.93872 + 0.69346I −13.16284 + 0.10930I
u = −1.42878 − 0.22236I
a = 0.635513 − 0.360503I
b = −0.044798 − 0.642597I
−3.93872 − 0.69346I −13.16284 − 0.10930I
u = 0.353961 + 0.248880I
a = 0.60428 + 1.70616I
b = 0.444558 + 1.167630I
−1.30454 + 3.85459I −7.72386 − 6.55740I
u = 0.353961 − 0.248880I
a = 0.60428 − 1.70616I
b = 0.444558 − 1.167630I
−1.30454 − 3.85459I −7.72386 + 6.55740I
u = 0.112509 + 0.356697I
a = 3.67512 − 2.27930I
b = 0.086415 − 0.687232I
1.35323 + 1.56259I −12.20805 − 3.14313I
u = 0.112509 − 0.356697I
a = 3.67512 + 2.27930I
b = 0.086415 + 0.687232I
1.35323 − 1.56259I −12.20805 + 3.14313I
u = −1.62694 + 0.05058I
a = −0.334359 − 0.989140I
b = 0.609573 − 1.022040I
−8.63988 − 2.65005I −12.70208 − 1.23601I
u = −1.62694 − 0.05058I
a = −0.334359 + 0.989140I
b = 0.609573 + 1.022040I
−8.63988 + 2.65005I −12.70208 + 1.23601I
u = 1.81475
a = −0.0145195
b = −0.559404
−15.9196 −0.921900
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
19
− 16u
18
+ ··· + 9u − 1)(u
24
+ 60u
23
+ ··· + 3708160u + 295936)
c
2
(u
19
− 8u
17
+ ··· + u + 1)(u
24
− 10u
23
+ ··· + 16u + 544)
c
3
(u
19
− 12u
17
+ ··· + 4u + 1)(u
24
− u
23
+ ··· − 289u + 143)
c
4
(u
19
− 2u
18
+ ··· + 5u
2
+ 1)(u
24
+ 3u
23
+ ··· − 327u − 41)
c
5
(u
19
+ 3u
18
+ ··· − 6u
2
− 1)(u
24
+ 2u
23
+ ··· + 13u − 1)
c
6
(u
19
+ 2u
17
+ ··· − u − 1)(u
24
− u
23
+ ··· − 288u − 69)
c
7
(u
19
− 8u
17
+ ··· + u − 1)(u
24
− 10u
23
+ ··· + 16u + 544)
c
8
(u
19
− 3u
18
+ ··· + 6u
2
+ 1)(u
24
+ 2u
23
+ ··· + 13u − 1)
c
9
, c
10
(u
19
− 12u
17
+ ··· + 4u − 1)(u
24
− u
23
+ ··· − 289u + 143)
c
11
(u
19
+ 2u
17
+ ··· − u + 1)(u
24
− u
23
+ ··· − 288u − 69)
c
12
(u
19
− u
18
+ ··· − 39u − 169)(u
24
− 36u
22
+ ··· − 47638u − 14543)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
19
− 32y
18
+ ··· − 19y −1)
· (y
24
− 296y
23
+ ··· − 4939910283264y + 87578116096)
c
2
, c
7
(y
19
− 16y
18
+ ··· + 9y −1)(y
24
− 60y
23
+ ··· − 3708160y + 295936)
c
3
, c
9
, c
10
(y
19
− 24y
18
+ ··· − 4y
2
− 1)(y
24
− 45y
23
+ ··· − 70079y + 20449)
c
4
(y
19
+ 6y
18
+ ··· − 10y −1)(y
24
− 11y
23
+ ··· − 33785y + 1681)
c
5
, c
8
(y
19
+ 7y
18
+ ··· − 12y −1)(y
24
+ 26y
23
+ ··· − 575y + 1)
c
6
, c
11
(y
19
+ 4y
18
+ ··· − 13y −1)(y
24
− 9y
23
+ ··· − 35058y + 4761)
c
12
(y
19
− 7y
18
+ ··· − 20111y −28561)
· (y
24
− 72y
23
+ ··· − 2969653580y + 211498849)
14
