12a
1015
(K12a
1015
)
A knot diagram
1
Linearized knot diagam
4 6 1 10 9 11 12 2 5 3 7 8
Solving Sequence
4,10 2,5
1 3 11 9 6 7 8 12
c
4
c
1
c
3
c
10
c
9
c
5
c
6
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.55158 × 10
71
u
69
− 2.48630 × 10
71
u
68
+ ··· + 4.14466 × 10
73
b + 4.49840 × 10
73
,
− 5.30555 × 10
74
u
69
− 8.22334 × 10
74
u
68
+ ··· + 4.55913 × 10
74
a + 1.52184 × 10
74
, u
70
+ 2u
69
+ ··· − 2u − 1i
I
u
2
= hb + 1, 6u
4
− u
3
+ 4u
2
+ 11a − 6u + 2, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 75 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
= h6.55×10
71
u
69
−2.49×10
71
u
68
+· · ·+4.14×10
73
b+4.50×10
73
, −5.31×
10
74
u
69
−8.22×10
74
u
68
+· · ·+4.56×10
74
a+1.52×10
74
, u
70
+2u
69
+· · ·−2u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
1.16372u
69
+ 1.80371u
68
+ ··· − 12.1418u − 0.333801
−0.0158073u
69
+ 0.00599879u
68
+ ··· + 0.128028u − 1.08535
a
5
=
1
u
2
a
1
=
1.14791u
69
+ 1.80971u
68
+ ··· − 12.0137u − 1.41915
−0.0158073u
69
+ 0.00599879u
68
+ ··· + 0.128028u − 1.08535
a
3
=
1.16769u
69
+ 1.80098u
68
+ ··· − 12.0610u − 0.269803
0.0108796u
69
+ 0.0526221u
68
+ ··· + 0.0867825u − 1.10387
a
11
=
1.23789u
69
+ 2.97447u
68
+ ··· − 8.93000u − 7.95394
−0.537189u
69
− 1.02248u
68
+ ··· + 3.28194u + 1.05622
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−0.232208u
69
− 0.851321u
68
+ ··· − 2.00060u + 4.73175
0.525839u
69
+ 0.960044u
68
+ ··· − 1.03476u − 0.695269
a
8
=
1.12189u
69
+ 2.81589u
68
+ ··· − 3.33901u − 8.52558
−0.674930u
69
− 1.33241u
68
+ ··· + 3.69661u + 1.16196
a
12
=
1.19605u
69
+ 2.08859u
68
+ ··· − 8.12152u − 5.32037
−0.265234u
69
− 0.371359u
68
+ ··· + 1.22176u − 0.304010
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.38477u
69
+ 8.26850u
68
+ ··· − 26.9142u − 8.59413
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
70
− 6u
69
+ ··· + 1478u − 121
c
2
u
70
− 5u
69
+ ··· − 29568u + 3872
c
4
, c
5
, c
9
u
70
+ 2u
69
+ ··· − 2u − 1
c
6
, c
7
, c
11
c
12
u
70
+ 2u
69
+ ··· − 2u + 1
c
8
11(11u
70
− 25u
69
+ ··· − 132109u − 43949)
c
10
11(11u
70
− 8u
69
+ ··· + 29588u + 17257)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
70
− 34y
69
+ ··· − 90458y + 14641
c
2
y
70
− 33y
69
+ ··· − 229160448y + 14992384
c
4
, c
5
, c
9
y
70
+ 66y
69
+ ··· − 4y + 1
c
6
, c
7
, c
11
c
12
y
70
− 82y
69
+ ··· − 4y + 1
c
8
121(121y
70
− 3045y
69
+ ··· − 4.12871 × 10
10
y + 1.93151 × 10
9
)
c
10
121(121y
70
+ 4358y
69
+ ··· + 3.69634 × 10
9
y + 2.97804 × 10
8
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.686400 + 0.713366I
a = −0.053948 − 0.210944I
b = 0.951229 − 0.454660I
0.87667 + 3.35580I 0
u = 0.686400 − 0.713366I
a = −0.053948 + 0.210944I
b = 0.951229 + 0.454660I
0.87667 − 3.35580I 0
u = −0.713932 + 0.648184I
a = −0.188351 + 0.239557I
b = 1.094430 + 0.592356I
8.96389 − 6.20258I 0
u = −0.713932 − 0.648184I
a = −0.188351 − 0.239557I
b = 1.094430 − 0.592356I
8.96389 + 6.20258I 0
u = −0.597225 + 0.868784I
a = 0.131337 + 0.213010I
b = 0.779698 + 0.239595I
−0.594033 + 1.028690I 0
u = −0.597225 − 0.868784I
a = 0.131337 − 0.213010I
b = 0.779698 − 0.239595I
−0.594033 − 1.028690I 0
u = −0.844565 + 0.393225I
a = 0.756345 + 0.697914I
b = 1.027460 − 0.439585I
−1.98877 + 4.08537I 0. − 6.03382I
u = −0.844565 − 0.393225I
a = 0.756345 − 0.697914I
b = 1.027460 + 0.439585I
−1.98877 − 4.08537I 0. + 6.03382I
u = 0.816696 + 0.440810I
a = 0.730245 − 0.900336I
b = 1.155090 + 0.559766I
0.05014 − 8.48498I 0. + 9.02977I
u = 0.816696 − 0.440810I
a = 0.730245 + 0.900336I
b = 1.155090 − 0.559766I
0.05014 + 8.48498I 0. − 9.02977I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.797710 + 0.463395I
a = 0.733935 + 1.050130I
b = 1.238960 − 0.666041I
8.39434 + 11.28920I 0. − 7.45273I
u = −0.797710 − 0.463395I
a = 0.733935 − 1.050130I
b = 1.238960 + 0.666041I
8.39434 − 11.28920I 0. + 7.45273I
u = 0.794883 + 0.243299I
a = 0.990789 − 0.382417I
b = 0.722317 + 0.329197I
1.74452 − 0.22556I 6.21604 + 2.91678I
u = 0.794883 − 0.243299I
a = 0.990789 + 0.382417I
b = 0.722317 − 0.329197I
1.74452 + 0.22556I 6.21604 − 2.91678I
u = −0.578794 + 0.475444I
a = −0.214985 − 0.392745I
b = 0.298756 + 1.109540I
11.29930 + 5.03905I 6.42974 − 5.21383I
u = −0.578794 − 0.475444I
a = −0.214985 + 0.392745I
b = 0.298756 − 1.109540I
11.29930 − 5.03905I 6.42974 + 5.21383I
u = −0.077426 + 1.268050I
a = 1.26161 − 1.02736I
b = −1.67281 + 0.43951I
7.81603 + 2.12622I 0
u = −0.077426 − 1.268050I
a = 1.26161 + 1.02736I
b = −1.67281 − 0.43951I
7.81603 − 2.12622I 0
u = −0.631247 + 0.350474I
a = 1.50034 + 0.57008I
b = 0.428001 − 0.725712I
10.93100 − 1.15018I 6.37418 − 2.37950I
u = −0.631247 − 0.350474I
a = 1.50034 − 0.57008I
b = 0.428001 + 0.725712I
10.93100 + 1.15018I 6.37418 + 2.37950I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514246 + 1.178650I
a = 0.234389 − 0.422329I
b = 0.777133 + 0.038992I
4.70260 − 4.51481I 0
u = 0.514246 − 1.178650I
a = 0.234389 + 0.422329I
b = 0.777133 − 0.038992I
4.70260 + 4.51481I 0
u = 0.514025 + 0.489099I
a = −0.032586 + 0.387308I
b = 0.207073 − 0.842044I
2.79286 − 3.41411I 6.06553 + 7.18074I
u = 0.514025 − 0.489099I
a = −0.032586 − 0.387308I
b = 0.207073 + 0.842044I
2.79286 + 3.41411I 6.06553 − 7.18074I
u = 0.027572 + 1.293330I
a = 0.713439 + 0.469428I
b = −1.50053 − 0.15574I
1.11976 − 1.25245I 0
u = 0.027572 − 1.293330I
a = 0.713439 − 0.469428I
b = −1.50053 + 0.15574I
1.11976 + 1.25245I 0
u = 0.094528 + 1.350430I
a = 0.61333 + 1.65329I
b = −1.103700 − 0.576201I
2.07680 − 1.88125I 0
u = 0.094528 − 1.350430I
a = 0.61333 − 1.65329I
b = −1.103700 + 0.576201I
2.07680 + 1.88125I 0
u = −0.133575 + 1.362630I
a = 0.64422 − 1.85435I
b = −0.974789 + 0.908157I
3.26167 + 4.51191I 0
u = −0.133575 − 1.362630I
a = 0.64422 + 1.85435I
b = −0.974789 − 0.908157I
3.26167 − 4.51191I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.161960 + 1.367850I
a = 0.56308 + 2.05596I
b = −0.91957 − 1.18906I
10.78790 − 5.95071I 0
u = 0.161960 − 1.367850I
a = 0.56308 − 2.05596I
b = −0.91957 + 1.18906I
10.78790 + 5.95071I 0
u = −0.057325 + 1.397340I
a = 0.79387 − 2.50536I
b = −0.854433 + 0.178775I
4.63360 + 0.45945I 0
u = −0.057325 − 1.397340I
a = 0.79387 + 2.50536I
b = −0.854433 − 0.178775I
4.63360 − 0.45945I 0
u = 0.05431 + 1.42323I
a = 2.44209 + 2.39720I
b = −0.772974 + 0.037973I
12.68320 + 0.08405I 0
u = 0.05431 − 1.42323I
a = 2.44209 − 2.39720I
b = −0.772974 − 0.037973I
12.68320 − 0.08405I 0
u = 0.575705
a = 1.22607
b = 0.312657
1.70984 5.97300
u = 0.522828 + 0.213932I
a = −0.301618 + 0.925186I
b = −1.078510 − 0.834623I
5.80188 − 3.48693I 0.21256 + 6.26702I
u = 0.522828 − 0.213932I
a = −0.301618 − 0.925186I
b = −1.078510 + 0.834623I
5.80188 + 3.48693I 0.21256 − 6.26702I
u = −0.27390 + 1.43660I
a = 0.53012 + 1.40501I
b = 0.798447 − 0.686186I
16.5894 + 2.2326I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27390 − 1.43660I
a = 0.53012 − 1.40501I
b = 0.798447 + 0.686186I
16.5894 − 2.2326I 0
u = −0.296415 + 0.442080I
a = 0.505486 − 0.384301I
b = 0.011825 + 0.286358I
0.074574 + 0.954323I 1.69242 − 6.62051I
u = −0.296415 − 0.442080I
a = 0.505486 + 0.384301I
b = 0.011825 − 0.286358I
0.074574 − 0.954323I 1.69242 + 6.62051I
u = −0.516350
a = −0.747230
b = −1.59427
4.13003 −2.66790
u = 0.31116 + 1.45838I
a = 0.165497 − 1.346330I
b = 0.987560 + 0.582127I
7.32955 − 4.26678I 0
u = 0.31116 − 1.45838I
a = 0.165497 + 1.346330I
b = 0.987560 − 0.582127I
7.32955 + 4.26678I 0
u = 0.18529 + 1.48231I
a = −0.56128 + 1.40862I
b = 0.350564 − 1.174690I
9.18672 − 6.01404I 0
u = 0.18529 − 1.48231I
a = −0.56128 − 1.40862I
b = 0.350564 + 1.174690I
9.18672 + 6.01404I 0
u = −0.20329 + 1.48122I
a = −0.76720 − 1.54412I
b = 0.44380 + 1.35657I
17.6404 + 7.9075I 0
u = −0.20329 − 1.48122I
a = −0.76720 + 1.54412I
b = 0.44380 − 1.35657I
17.6404 − 7.9075I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.465530 + 0.181096I
a = −0.482595 − 1.101610I
b = −1.074710 + 0.528711I
−1.59167 + 2.36731I −3.11903 − 9.00869I
u = −0.465530 − 0.181096I
a = −0.482595 + 1.101610I
b = −1.074710 − 0.528711I
−1.59167 − 2.36731I −3.11903 + 9.00869I
u = −0.15387 + 1.49344I
a = −0.313268 − 1.110630I
b = 0.304389 + 0.861897I
6.62342 + 2.84491I 0
u = −0.15387 − 1.49344I
a = −0.313268 + 1.110630I
b = 0.304389 − 0.861897I
6.62342 − 2.84491I 0
u = −0.31045 + 1.49001I
a = −0.09717 + 1.48789I
b = 1.160460 − 0.608170I
4.10310 + 8.26194I 0
u = −0.31045 − 1.49001I
a = −0.09717 − 1.48789I
b = 1.160460 + 0.608170I
4.10310 − 8.26194I 0
u = 0.212174 + 0.423840I
a = 3.71972 + 1.14676I
b = −1.020370 + 0.337236I
6.92279 + 1.01855I 7.26660 + 6.17697I
u = 0.212174 − 0.423840I
a = 3.71972 − 1.14676I
b = −1.020370 − 0.337236I
6.92279 − 1.01855I 7.26660 − 6.17697I
u = 0.29881 + 1.50168I
a = −0.19283 − 1.67138I
b = 1.25053 + 0.69071I
6.33511 − 12.54100I 0
u = 0.29881 − 1.50168I
a = −0.19283 + 1.67138I
b = 1.25053 − 0.69071I
6.33511 + 12.54100I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.29039 + 1.50769I
a = −0.24071 + 1.82752I
b = 1.30886 − 0.76850I
14.7792 + 15.2576I 0
u = −0.29039 − 1.50769I
a = −0.24071 − 1.82752I
b = 1.30886 + 0.76850I
14.7792 − 15.2576I 0
u = 0.15367 + 1.54248I
a = −0.510964 + 0.695006I
b = 0.606981 − 0.660450I
8.47071 + 0.57802I 0
u = 0.15367 − 1.54248I
a = −0.510964 − 0.695006I
b = 0.606981 + 0.660450I
8.47071 − 0.57802I 0
u = −0.18664 + 1.56544I
a = −0.799854 − 0.540948I
b = 0.866770 + 0.671583I
16.3833 − 2.9707I 0
u = −0.18664 − 1.56544I
a = −0.799854 + 0.540948I
b = 0.866770 − 0.671583I
16.3833 + 2.9707I 0
u = 0.410685 + 0.072099I
a = −1.48188 + 0.86518I
b = −1.199220 − 0.163900I
−2.39243 − 0.16622I −6.14498 − 3.46672I
u = 0.410685 − 0.072099I
a = −1.48188 − 0.86518I
b = −1.199220 + 0.163900I
−2.39243 + 0.16622I −6.14498 + 3.46672I
u = −0.176628 + 0.303504I
a = 4.01544 − 3.09185I
b = −0.957887 − 0.108785I
−0.643301 − 0.452052I 0.8141 − 14.9412I
u = −0.176628 − 0.303504I
a = 4.01544 + 3.09185I
b = −0.957887 + 0.108785I
−0.643301 + 0.452052I 0.8141 + 14.9412I
11
II. I
u
2
= hb + 1, 6u
4
− u
3
+ 4u
2
+ 11a − 6u + 2, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
−0.545455u
4
+ 0.0909091u
3
+ ··· + 0.545455u − 0.181818
−1
a
5
=
1
u
2
a
1
=
−0.545455u
4
+ 0.0909091u
3
+ ··· + 0.545455u − 1.18182
−1
a
3
=
−0.545455u
4
+ 0.0909091u
3
+ ··· + 0.545455u − 0.181818
−1
a
11
=
0.280992u
4
− 0.0165289u
3
+ ··· + 0.0826446u + 0.487603
0.636364u
4
+ 0.727273u
3
+ ··· + 1.36364u + 0.545455
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
0.157025u
4
+ 0.0495868u
3
+ ··· − 0.247934u + 1.53719
0.0909091u
4
− 0.181818u
3
+ ··· − 0.0909091u + 0.363636
a
8
=
−0.0991736u
4
− 0.347107u
3
+ ··· + 0.735537u + 0.239669
0.363636u
4
+ 1.27273u
3
+ ··· + 1.63636u + 0.454545
a
12
=
−1.24793u
4
+ 0.132231u
3
+ ··· + 0.338843u − 0.900826
−1.09091u
4
− 0.818182u
3
+ ··· + 0.0909091u − 1.36364
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
121
u
4
+
349
121
u
3
+
441
121
u
2
+
554
121
u −
71
121
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
u
5
c
3
(u + 1)
5
c
4
, c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
, c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
11(11u
5
− 2u
4
+ 6u
3
+ u
2
+ 1)
c
9
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
10
11(11u
5
+ 13u
4
− 3u
2
+ u + 1)
c
11
, c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
5
c
2
y
5
c
4
, c
5
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
7
, c
11
c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
121(121y
5
+ 128y
4
+ 40y
3
+ 3y
2
− 2y −1)
c
10
121(121y
5
− 169y
4
+ 100y
3
− 35y
2
+ 7y −1)
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 0.146090 + 0.562510I
b = −1.00000
−1.31583 − 1.53058I −2.95202 + 5.03288I
u = 0.339110 − 0.822375I
a = 0.146090 − 0.562510I
b = −1.00000
−1.31583 + 1.53058I −2.95202 − 5.03288I
u = −0.766826
a = −1.04351
b = −1.00000
0.756147 −3.26660
u = −0.455697 + 1.200150I
a = 0.012026 − 0.507727I
b = −1.00000
4.22763 + 4.40083I −1.77007 − 1.41023I
u = −0.455697 − 1.200150I
a = 0.012026 + 0.507727I
b = −1.00000
4.22763 − 4.40083I −1.77007 + 1.41023I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
70
− 6u
69
+ ··· + 1478u − 121)
c
2
u
5
(u
70
− 5u
69
+ ··· − 29568u + 3872)
c
3
((u + 1)
5
)(u
70
− 6u
69
+ ··· + 1478u − 121)
c
4
, c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
70
+ 2u
69
+ ··· − 2u − 1)
c
6
, c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
70
+ 2u
69
+ ··· − 2u + 1)
c
8
121(11u
5
− 2u
4
+ 6u
3
+ u
2
+ 1)
· (11u
70
− 25u
69
+ ··· − 132109u − 43949)
c
9
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
70
+ 2u
69
+ ··· − 2u − 1)
c
10
121(11u
5
+ 13u
4
− 3u
2
+ u + 1)
· (11u
70
− 8u
69
+ ··· + 29588u + 17257)
c
11
, c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
70
+ 2u
69
+ ··· − 2u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
5
)(y
70
− 34y
69
+ ··· − 90458y + 14641)
c
2
y
5
(y
70
− 33y
69
+ ··· − 2.29160 × 10
8
y + 1.49924 × 10
7
)
c
4
, c
5
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
70
+ 66y
69
+ ··· − 4y + 1)
c
6
, c
7
, c
11
c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
70
− 82y
69
+ ··· − 4y + 1)
c
8
14641(121y
5
+ 128y
4
+ 40y
3
+ 3y
2
− 2y −1)
· (121y
70
− 3045y
69
+ ··· − 41287121663y + 1931514601)
c
10
14641(121y
5
− 169y
4
+ 100y
3
− 35y
2
+ 7y −1)
· (121y
70
+ 4358y
69
+ ··· + 3696343724y + 297804049)
17
