12a
1254
(K12a
1254
)
A knot diagram
1
Linearized knot diagam
5 7 8 1 10 11 3 12 2 6 4 9
Solving Sequence
5,10
6 11
2,7
3 1 4 9 12 8
c
5
c
10
c
6
c
2
c
1
c
4
c
9
c
12
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.63090 × 10
126
u
71
− 1.43198 × 10
127
u
70
+ ··· + 1.61786 × 10
128
b + 1.62123 × 10
128
,
− 1.10105 × 10
130
u
71
− 3.48895 × 10
130
u
70
+ ··· + 3.39751 × 10
129
a + 5.30987 × 10
130
,
u
72
+ 3u
71
+ ··· − 26u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 72 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−1.63 × 10
126
u
71
− 1.43 × 10
127
u
70
+ · · · + 1.62 × 10
128
b + 1.62 ×
10
128
, −1.10 × 10
130
u
71
− 3.49 × 10
130
u
70
+ · · · + 3.40 × 10
129
a + 5.31 ×
10
130
, u
72
+ 3u
71
+ · · · − 26u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
3.24076u
71
+ 10.2691u
70
+ ··· − 136.064u − 15.6287
0.0100806u
71
+ 0.0885108u
70
+ ··· + 0.154524u − 1.00208
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
3.01036u
71
+ 9.56914u
70
+ ··· − 129.487u − 15.8619
0.0443474u
71
+ 0.191702u
70
+ ··· + 0.547558u − 0.927506
a
1
=
3.25084u
71
+ 10.3576u
70
+ ··· − 135.909u − 16.6308
0.0100806u
71
+ 0.0885108u
70
+ ··· + 0.154524u − 1.00208
a
4
=
3.93995u
71
+ 12.1793u
70
+ ··· − 144.274u − 18.1963
−0.205083u
71
− 0.696225u
70
+ ··· − 1.51684u − 0.931392
a
9
=
25.0206u
71
+ 79.2187u
70
+ ··· − 1012.78u − 151.398
0.440428u
71
+ 1.31089u
70
+ ··· − 17.2649u − 4.14504
a
12
=
28.8160u
71
+ 90.4805u
70
+ ··· − 1156.38u − 175.392
0.437569u
71
+ 1.27882u
70
+ ··· − 21.8953u − 4.40858
a
8
=
−3.44954u
71
− 11.3202u
70
+ ··· + 159.467u + 31.2821
−0.193079u
71
− 0.610090u
70
+ ··· + 6.79834u − 0.0918382
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.04864u
71
+ 17.1634u
70
+ ··· − 197.061u − 30.2965
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
72
+ u
71
+ ··· − 16u + 1
c
2
, c
3
, c
7
u
72
+ 3u
71
+ ··· − 26u
2
+ 1
c
5
, c
6
, c
10
u
72
− 3u
71
+ ··· − 26u
2
+ 1
c
8
, c
12
u
72
− u
71
+ ··· + 16u + 1
c
9
63(63u
72
+ 1197u
71
+ ··· − 137930u − 101308)
c
11
63(63u
72
− 1197u
71
+ ··· + 137930u − 101308)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
12
y
72
− 51y
71
+ ··· − 20y + 1
c
2
, c
3
, c
5
c
6
, c
7
, c
10
y
72
− 71y
71
+ ··· − 52y + 1
c
9
, c
11
3969
· (3969y
72
− 532791y
71
+ ··· + 24968314100y + 10263310864)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.649955 + 0.767013I
a = 0.371690 + 0.863674I
b = −1.157260 − 0.177201I
−3.51621 − 2.84598I 0
u = 0.649955 − 0.767013I
a = 0.371690 − 0.863674I
b = −1.157260 + 0.177201I
−3.51621 + 2.84598I 0
u = 0.755046 + 0.607683I
a = 0.958639 − 0.782753I
b = 0.211107 + 0.677137I
9.48984 + 1.78690I 0
u = 0.755046 − 0.607683I
a = 0.958639 + 0.782753I
b = 0.211107 − 0.677137I
9.48984 − 1.78690I 0
u = 0.561764 + 0.889787I
a = −0.343337 − 1.311210I
b = 1.285200 + 0.503327I
6.85180 − 11.78730I 0
u = 0.561764 − 0.889787I
a = −0.343337 + 1.311210I
b = 1.285200 − 0.503327I
6.85180 + 11.78730I 0
u = −0.566060 + 0.689487I
a = 0.38171 − 1.40245I
b = −1.258670 + 0.517373I
8.38473I 0
u = −0.566060 − 0.689487I
a = 0.38171 + 1.40245I
b = −1.258670 − 0.517373I
− 8.38473I 0
u = −0.401846 + 0.784856I
a = 0.911206 − 0.151398I
b = −1.075360 − 0.313339I
0.50187 − 3.59150I 0. + 6.84899I
u = −0.401846 − 0.784856I
a = 0.911206 + 0.151398I
b = −1.075360 + 0.313339I
0.50187 + 3.59150I 0. − 6.84899I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.360230 + 0.755264I
a = −0.121619 + 1.340780I
b = 0.060046 − 1.002070I
10.66310 − 6.45840I 7.25218 + 5.11414I
u = 0.360230 − 0.755264I
a = −0.121619 − 1.340780I
b = 0.060046 + 1.002070I
10.66310 + 6.45840I 7.25218 − 5.11414I
u = 0.649376 + 0.994071I
a = −0.537633 + 0.012831I
b = 1.131150 − 0.361477I
6.71683 + 5.69927I 0
u = 0.649376 − 0.994071I
a = −0.537633 − 0.012831I
b = 1.131150 + 0.361477I
6.71683 − 5.69927I 0
u = −0.474762 + 1.140520I
a = −0.524061 + 0.650730I
b = 1.171890 − 0.205962I
1.64587 + 4.92294I 0
u = −0.474762 − 1.140520I
a = −0.524061 − 0.650730I
b = 1.171890 + 0.205962I
1.64587 − 4.92294I 0
u = −0.208137 + 0.704884I
a = 0.708628 − 1.104090I
b = −0.091169 + 0.449600I
5.21021 + 2.48118I 6.35115 − 4.16718I
u = −0.208137 − 0.704884I
a = 0.708628 + 1.104090I
b = −0.091169 − 0.449600I
5.21021 − 2.48118I 6.35115 + 4.16718I
u = −1.267630 + 0.242344I
a = 0.752454 − 0.638834I
b = −0.101250 + 0.346802I
2.11200 + 1.03313I 0
u = −1.267630 − 0.242344I
a = 0.752454 + 0.638834I
b = −0.101250 − 0.346802I
2.11200 − 1.03313I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32452
a = −0.890875
b = −2.07992
2.49962 0
u = −1.346220 + 0.078526I
a = −0.291387 + 0.201598I
b = −1.38956 − 1.17852I
1.46224 + 2.61815I 0
u = −1.346220 − 0.078526I
a = −0.291387 − 0.201598I
b = −1.38956 + 1.17852I
1.46224 − 2.61815I 0
u = 1.363600 + 0.025152I
a = −0.513667 − 0.148824I
b = −0.113437 + 0.094897I
−3.19701 − 0.01303I 0
u = 1.363600 − 0.025152I
a = −0.513667 + 0.148824I
b = −0.113437 − 0.094897I
−3.19701 + 0.01303I 0
u = −1.37923
a = −1.92010
b = −1.32845
−1.08828 0
u = 0.434671 + 0.429294I
a = −0.56763 − 1.50065I
b = 1.215410 + 0.596589I
−0.50187 − 3.59150I −0.30026 + 6.84899I
u = 0.434671 − 0.429294I
a = −0.56763 + 1.50065I
b = 1.215410 − 0.596589I
−0.50187 + 3.59150I −0.30026 − 6.84899I
u = 1.388510 + 0.125096I
a = 0.295480 − 0.465640I
b = 0.27946 + 1.49621I
−1.64587 − 4.92294I 0
u = 1.388510 − 0.125096I
a = 0.295480 + 0.465640I
b = 0.27946 − 1.49621I
−1.64587 + 4.92294I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.398290 + 0.071099I
a = 0.058738 − 0.776258I
b = −0.912296 + 0.581047I
−2.11200 − 1.03313I 0
u = 1.398290 − 0.071099I
a = 0.058738 + 0.776258I
b = −0.912296 − 0.581047I
−2.11200 + 1.03313I 0
u = −0.551714 + 0.218194I
a = 0.121797 + 0.972740I
b = 1.181600 − 0.138253I
−2.64681 + 0.31493I −3.09974 + 2.98415I
u = −0.551714 − 0.218194I
a = 0.121797 − 0.972740I
b = 1.181600 + 0.138253I
−2.64681 − 0.31493I −3.09974 − 2.98415I
u = −1.404890 + 0.097683I
a = 0.063758 + 0.734444I
b = 0.395294 − 0.764529I
−5.21021 + 2.48118I 0
u = −1.404890 − 0.097683I
a = 0.063758 − 0.734444I
b = 0.395294 + 0.764529I
−5.21021 − 2.48118I 0
u = 1.40558 + 0.24747I
a = −0.083482 + 0.851271I
b = −0.216127 − 0.825464I
− 5.89665I 0
u = 1.40558 − 0.24747I
a = −0.083482 − 0.851271I
b = −0.216127 + 0.825464I
5.89665I 0
u = −0.501776 + 0.266487I
a = −1.68326 − 0.64048I
b = −0.349712 + 0.435136I
2.64681 − 0.31493I 3.09974 − 2.98415I
u = −0.501776 − 0.266487I
a = −1.68326 + 0.64048I
b = −0.349712 − 0.435136I
2.64681 + 0.31493I 3.09974 + 2.98415I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44069
a = 6.02414
b = 1.02295
−4.98750 0
u = −1.44554 + 0.26940I
a = −0.382483 − 0.613995I
b = −0.139489 + 1.196830I
4.86838 + 10.14510I 0
u = −1.44554 − 0.26940I
a = −0.382483 + 0.613995I
b = −0.139489 − 1.196830I
4.86838 − 10.14510I 0
u = −0.246051 + 0.465180I
a = 0.19086 + 1.49758I
b = −0.139532 − 1.090770I
3.51621 + 2.84598I 7.08728 − 8.53827I
u = −0.246051 − 0.465180I
a = 0.19086 − 1.49758I
b = −0.139532 + 1.090770I
3.51621 − 2.84598I 7.08728 + 8.53827I
u = −1.47163 + 0.14528I
a = 0.565549 + 0.814669I
b = 1.57798 − 0.67208I
−6.71683 + 5.69927I 0
u = −1.47163 − 0.14528I
a = 0.565549 − 0.814669I
b = 1.57798 + 0.67208I
−6.71683 − 5.69927I 0
u = 1.51164 + 0.11669I
a = 0.684539 − 0.713923I
b = 1.44150 + 0.28466I
−9.48984 − 1.78690I 0
u = 1.51164 − 0.11669I
a = 0.684539 + 0.713923I
b = 1.44150 − 0.28466I
−9.48984 + 1.78690I 0
u = 0.227486 + 0.392172I
a = −2.91334 − 1.86372I
b = 0.976660 − 0.216723I
0.906236I 0. + 9.31169I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227486 − 0.392172I
a = −2.91334 + 1.86372I
b = 0.976660 + 0.216723I
− 0.906236I 0. − 9.31169I
u = 1.53124 + 0.23600I
a = −0.569957 + 1.044770I
b = −1.46206 − 0.58160I
−6.85180 − 11.78730I 0
u = 1.53124 − 0.23600I
a = −0.569957 − 1.044770I
b = −1.46206 + 0.58160I
−6.85180 + 11.78730I 0
u = −1.55559
a = 1.08766
b = −0.193111
1.08828 0
u = −1.54857 + 0.24062I
a = −0.476741 − 0.923449I
b = −1.38209 + 0.33972I
−10.66310 + 6.45840I 0
u = −1.54857 − 0.24062I
a = −0.476741 + 0.923449I
b = −1.38209 − 0.33972I
−10.66310 − 6.45840I 0
u = 0.216451 + 0.368593I
a = −0.516118 − 0.919730I
b = 0.122854 + 0.327294I
− 0.846056I 0. + 8.06993I
u = 0.216451 − 0.368593I
a = −0.516118 + 0.919730I
b = 0.122854 − 0.327294I
0.846056I 0. − 8.06993I
u = −1.55377 + 0.31543I
a = 0.587127 + 1.178050I
b = 1.42437 − 0.53718I
16.1961I 0
u = −1.55377 − 0.31543I
a = 0.587127 − 1.178050I
b = 1.42437 + 0.53718I
− 16.1961I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54410 + 0.36847I
a = 0.336253 − 1.043030I
b = 1.350500 + 0.365176I
−4.86838 − 10.14510I 0
u = 1.54410 − 0.36847I
a = 0.336253 + 1.043030I
b = 1.350500 − 0.365176I
−4.86838 + 10.14510I 0
u = 0.104562 + 0.393865I
a = 0.765029 − 1.020030I
b = −1.49104 + 0.54161I
5.95339 − 0.98579I 13.4814 + 6.1699I
u = 0.104562 − 0.393865I
a = 0.765029 + 1.020030I
b = −1.49104 − 0.54161I
5.95339 + 0.98579I 13.4814 − 6.1699I
u = 1.62235 + 0.28986I
a = −0.362610 + 0.552302I
b = −1.131580 − 0.066438I
−5.95339 − 0.98579I 0
u = 1.62235 − 0.28986I
a = −0.362610 − 0.552302I
b = −1.131580 + 0.066438I
−5.95339 + 0.98579I 0
u = −1.55311 + 0.67597I
a = −0.002070 + 0.554887I
b = 1.171780 − 0.109704I
−1.46224 + 2.61815I 0
u = −1.55311 − 0.67597I
a = −0.002070 − 0.554887I
b = 1.171780 + 0.109704I
−1.46224 − 2.61815I 0
u = −0.258714 + 0.094467I
a = 3.50898 + 1.82058I
b = −0.846426 − 0.103474I
3.19701 + 0.01303I 0.976771 + 0.960819I
u = −0.258714 − 0.094467I
a = 3.50898 − 1.82058I
b = −0.846426 + 0.103474I
3.19701 − 0.01303I 0.976771 − 0.960819I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.155044
a = −52.3313
b = −1.07077
4.98750 −83.9270
u = −1.95291
a = 0.284351
b = 1.16979
−2.49962 0
12
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
72
+ u
71
+ ··· − 16u + 1
c
2
, c
3
, c
7
u
72
+ 3u
71
+ ··· − 26u
2
+ 1
c
5
, c
6
, c
10
u
72
− 3u
71
+ ··· − 26u
2
+ 1
c
8
, c
12
u
72
− u
71
+ ··· + 16u + 1
c
9
63(63u
72
+ 1197u
71
+ ··· − 137930u − 101308)
c
11
63(63u
72
− 1197u
71
+ ··· + 137930u − 101308)
13
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
12
y
72
− 51y
71
+ ··· − 20y + 1
c
2
, c
3
, c
5
c
6
, c
7
, c
10
y
72
− 71y
71
+ ··· − 52y + 1
c
9
, c
11
3969
· (3969y
72
− 532791y
71
+ ··· + 24968314100y + 10263310864)
14
