12a
0277
(K12a
0277
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 11 5 4 1 12 7 10
Solving Sequence
1,9 5,10
4 8 3 2 7 12 11 6
c
9
c
4
c
8
c
3
c
1
c
7
c
12
c
10
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.72311 × 10
64
u
79
+ 9.32849 × 10
65
u
78
+ ··· + 1.78584 × 10
64
b + 1.98266 × 10
65
,
1.08221 × 10
65
u
79
− 2.14479 × 10
66
u
78
+ ··· + 1.78584 × 10
64
a − 3.42835 × 10
65
, u
80
− 20u
79
+ ··· − 18u + 1i
I
u
2
= hb
2
− 2, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
I
u
3
= hb, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 89 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−4.72 × 10
64
u
79
+ 9.33 × 10
65
u
78
+ · · · + 1.79 × 10
64
b + 1.98 ×
10
65
, 1.08 × 10
65
u
79
− 2.14 × 10
66
u
78
+ · · · + 1.79 × 10
64
a − 3.43 ×
10
65
, u
80
− 20u
79
+ · · · − 18u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−6.05997u
79
+ 120.100u
78
+ ··· − 283.148u + 19.1974
2.64476u
79
− 52.2359u
78
+ ··· + 160.871u − 11.1021
a
10
=
1
u
2
a
4
=
−3.41521u
79
+ 67.8640u
78
+ ··· − 122.277u + 8.09533
2.64476u
79
− 52.2359u
78
+ ··· + 160.871u − 11.1021
a
8
=
2.78759u
79
− 55.0401u
78
+ ··· + 4.23430u + 2.44867
−2.71435u
79
+ 53.7245u
78
+ ··· − 169.151u + 11.1549
a
3
=
3.75953u
79
− 74.3293u
78
+ ··· + 112.373u − 6.62197
−1.90562u
79
+ 37.5370u
78
+ ··· − 107.936u + 6.96219
a
2
=
−3.45746u
79
+ 68.4432u
78
+ ··· − 98.6276u + 5.02931
1.66130u
79
− 32.7533u
78
+ ··· + 100.748u − 6.43094
a
7
=
−4.58743u
79
+ 90.5934u
78
+ ··· − 281.163u + 21.8214
0.879640u
79
− 17.2874u
78
+ ··· + 40.9055u − 3.15319
a
12
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−3.15319u
79
+ 62.1841u
78
+ ··· − 201.223u + 15.8519
0.849761u
79
− 16.8147u
78
+ ··· + 48.0720u − 3.70779
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.49769u
79
− 108.641u
78
+ ··· + 342.310u − 39.1178
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
80
+ 38u
79
+ ··· + 15621u + 529
c
2
, c
5
u
80
+ 4u
79
+ ··· − 163u − 23
c
3
, c
4
, c
8
u
80
+ u
79
+ ··· − 8u − 8
c
6
, c
11
u
80
− 2u
79
+ ··· − 4u − 1
c
7
u
80
− 3u
79
+ ··· + 5400u + 1000
c
9
, c
10
, c
12
u
80
+ 20u
79
+ ··· + 18u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
80
+ 18y
79
+ ··· − 20758597y + 279841
c
2
, c
5
y
80
− 38y
79
+ ··· − 15621y + 529
c
3
, c
4
, c
8
y
80
− 73y
79
+ ··· + 576y + 64
c
6
, c
11
y
80
− 20y
79
+ ··· − 18y + 1
c
7
y
80
+ 11y
79
+ ··· + 9560000y + 1000000
c
9
, c
10
, c
12
y
80
+ 84y
79
+ ··· + 86y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514598 + 0.797614I
a = −0.182271 + 0.963044I
b = −0.166867 − 0.621031I
1.34935 − 2.65440I 0
u = 0.514598 − 0.797614I
a = −0.182271 − 0.963044I
b = −0.166867 + 0.621031I
1.34935 + 2.65440I 0
u = 0.930722 + 0.185711I
a = 0.009280 + 0.280137I
b = 0.181905 − 0.585150I
−2.18248 + 1.71695I 0
u = 0.930722 − 0.185711I
a = 0.009280 − 0.280137I
b = 0.181905 + 0.585150I
−2.18248 − 1.71695I 0
u = 0.919274 + 0.137908I
a = 0.747010 + 0.189533I
b = 1.288870 − 0.122433I
−5.31070 + 0.42006I 0
u = 0.919274 − 0.137908I
a = 0.747010 − 0.189533I
b = 1.288870 + 0.122433I
−5.31070 − 0.42006I 0
u = 1.030150 + 0.302517I
a = −0.848263 − 0.262462I
b = −1.366380 + 0.243133I
−7.10040 + 4.78774I 0
u = 1.030150 − 0.302517I
a = −0.848263 + 0.262462I
b = −1.366380 − 0.243133I
−7.10040 − 4.78774I 0
u = 0.609392 + 0.691381I
a = 0.204257 + 0.417749I
b = 0.629301 − 0.385404I
−1.82971 − 3.50991I 0
u = 0.609392 − 0.691381I
a = 0.204257 − 0.417749I
b = 0.629301 + 0.385404I
−1.82971 + 3.50991I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755355 + 0.786820I
a = 0.28069 − 1.41735I
b = 1.347050 + 0.254095I
−3.40751 − 5.86732I 0
u = 0.755355 − 0.786820I
a = 0.28069 + 1.41735I
b = 1.347050 − 0.254095I
−3.40751 + 5.86732I 0
u = 0.788627 + 0.790526I
a = 0.437053 − 0.837105I
b = 0.269993 + 0.717932I
−0.40460 − 7.35219I 0
u = 0.788627 − 0.790526I
a = 0.437053 + 0.837105I
b = 0.269993 − 0.717932I
−0.40460 + 7.35219I 0
u = 0.684330 + 0.553457I
a = 0.01541 + 2.37497I
b = −1.388830 − 0.162566I
−8.24545 − 2.75079I 0
u = 0.684330 − 0.553457I
a = 0.01541 − 2.37497I
b = −1.388830 + 0.162566I
−8.24545 + 2.75079I 0
u = −0.127842 + 0.864691I
a = −0.255160 + 0.396206I
b = 1.260690 + 0.244422I
−1.23948 − 4.76112I 0
u = −0.127842 − 0.864691I
a = −0.255160 − 0.396206I
b = 1.260690 − 0.244422I
−1.23948 + 4.76112I 0
u = 0.419774 + 1.097820I
a = 0.077772 − 0.334119I
b = 1.194940 + 0.059585I
−1.55006 − 4.38158I 0
u = 0.419774 − 1.097820I
a = 0.077772 + 0.334119I
b = 1.194940 − 0.059585I
−1.55006 + 4.38158I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680437 + 0.465530I
a = −0.917464 − 0.679063I
b = −1.47224 + 0.10694I
−8.51159 − 1.83203I 0
u = 0.680437 − 0.465530I
a = −0.917464 + 0.679063I
b = −1.47224 − 0.10694I
−8.51159 + 1.83203I 0
u = 0.894405 + 0.764372I
a = −0.61624 + 1.42654I
b = −1.40800 − 0.29107I
−5.74546 − 11.03100I 0
u = 0.894405 − 0.764372I
a = −0.61624 − 1.42654I
b = −1.40800 + 0.29107I
−5.74546 + 11.03100I 0
u = 0.289262 + 1.239150I
a = −0.045610 + 0.413852I
b = 0.023350 − 0.410951I
1.97481 − 2.69073I 0
u = 0.289262 − 1.239150I
a = −0.045610 − 0.413852I
b = 0.023350 + 0.410951I
1.97481 + 2.69073I 0
u = 0.590617 + 0.310506I
a = 0.96087 − 1.72410I
b = 0.255679 + 0.386530I
−2.98638 − 0.61275I 0
u = 0.590617 − 0.310506I
a = 0.96087 + 1.72410I
b = 0.255679 − 0.386530I
−2.98638 + 0.61275I 0
u = 0.454841 + 1.317990I
a = −0.1307020 + 0.0215197I
b = −1.299560 + 0.177427I
−2.13245 − 0.48191I 0
u = 0.454841 − 1.317990I
a = −0.1307020 − 0.0215197I
b = −1.299560 − 0.177427I
−2.13245 + 0.48191I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.181005 + 0.568134I
a = 0.897771 + 0.786811I
b = 0.002312 − 0.687422I
2.60603 − 1.37683I 0
u = −0.181005 − 0.568134I
a = 0.897771 − 0.786811I
b = 0.002312 + 0.687422I
2.60603 + 1.37683I 0
u = −0.134787 + 0.567278I
a = 0.180641 − 1.107910I
b = −1.039780 − 0.137065I
−0.586277 − 0.026228I 0
u = −0.134787 − 0.567278I
a = 0.180641 + 1.107910I
b = −1.039780 + 0.137065I
−0.586277 + 0.026228I 0
u = 0.06859 + 1.42466I
a = 0.0103422 + 0.0743670I
b = 1.53685 + 0.05092I
−1.92343 − 1.06909I 0
u = 0.06859 − 1.42466I
a = 0.0103422 − 0.0743670I
b = 1.53685 − 0.05092I
−1.92343 + 1.06909I 0
u = 0.02099 + 1.43824I
a = −1.27488 + 1.90471I
b = 1.284890 − 0.223646I
−1.128470 − 0.060432I 0
u = 0.02099 − 1.43824I
a = −1.27488 − 1.90471I
b = 1.284890 + 0.223646I
−1.128470 + 0.060432I 0
u = −0.13847 + 1.45741I
a = −0.22590 + 1.82988I
b = 1.42465 − 0.34186I
2.61988 + 9.27844I 0
u = −0.13847 − 1.45741I
a = −0.22590 − 1.82988I
b = 1.42465 + 0.34186I
2.61988 − 9.27844I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.460918 + 0.266517I
a = 2.09447 + 1.71266I
b = 1.368840 − 0.297213I
−3.08811 + 7.18574I −12.00000 − 5.24210I
u = −0.460918 − 0.266517I
a = 2.09447 − 1.71266I
b = 1.368840 + 0.297213I
−3.08811 − 7.18574I −12.00000 + 5.24210I
u = 0.14377 + 1.46363I
a = 0.03873 − 1.88336I
b = 0.025762 + 0.609131I
2.80366 − 3.04715I 0
u = 0.14377 − 1.46363I
a = 0.03873 + 1.88336I
b = 0.025762 − 0.609131I
2.80366 + 3.04715I 0
u = −0.361611 + 0.356179I
a = −1.186320 − 0.369766I
b = −0.184021 + 0.722514I
1.82614 + 3.48233I −6.79383 − 4.10527I
u = −0.361611 − 0.356179I
a = −1.186320 + 0.369766I
b = −0.184021 − 0.722514I
1.82614 − 3.48233I −6.79383 + 4.10527I
u = −0.09473 + 1.49234I
a = −0.37347 − 1.41277I
b = −0.273288 + 0.830850I
8.02170 + 5.03620I 0
u = −0.09473 − 1.49234I
a = −0.37347 + 1.41277I
b = −0.273288 − 0.830850I
8.02170 − 5.03620I 0
u = −0.07942 + 1.49484I
a = 0.49054 − 1.68999I
b = −1.352670 + 0.354404I
4.96185 + 3.39118I 0
u = −0.07942 − 1.49484I
a = 0.49054 + 1.68999I
b = −1.352670 − 0.354404I
4.96185 − 3.39118I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332942 + 0.368563I
a = −1.44289 − 2.26230I
b = −1.266150 + 0.253252I
−1.29040 + 2.02256I −9.24202 − 0.57616I
u = −0.332942 − 0.368563I
a = −1.44289 + 2.26230I
b = −1.266150 − 0.253252I
−1.29040 − 2.02256I −9.24202 + 0.57616I
u = −0.02150 + 1.51043I
a = 0.641454 + 0.593646I
b = −0.863283 − 0.509080I
6.14398 + 0.32762I 0
u = −0.02150 − 1.51043I
a = 0.641454 − 0.593646I
b = −0.863283 + 0.509080I
6.14398 − 0.32762I 0
u = 0.21180 + 1.49644I
a = −0.0472308 − 0.0518403I
b = −1.54021 + 0.06751I
−2.11984 − 5.02621I 0
u = 0.21180 − 1.49644I
a = −0.0472308 + 0.0518403I
b = −1.54021 − 0.06751I
−2.11984 + 5.02621I 0
u = −0.01749 + 1.53790I
a = 0.23906 + 1.46861I
b = 0.151849 − 0.830520I
9.69171 − 0.86841I 0
u = −0.01749 − 1.53790I
a = 0.23906 − 1.46861I
b = 0.151849 + 0.830520I
9.69171 + 0.86841I 0
u = 0.22890 + 1.53233I
a = 1.09093 + 1.88029I
b = −1.308650 − 0.236482I
−1.40415 − 6.10807I 0
u = 0.22890 − 1.53233I
a = 1.09093 − 1.88029I
b = −1.308650 + 0.236482I
−1.40415 + 6.10807I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06363 + 1.57023I
a = −0.768391 − 0.799066I
b = 1.049850 + 0.428553I
6.92564 − 5.37799I 0
u = 0.06363 − 1.57023I
a = −0.768391 + 0.799066I
b = 1.049850 − 0.428553I
6.92564 + 5.37799I 0
u = 0.11638 + 1.58430I
a = 0.708844 − 0.840566I
b = −1.010650 + 0.434495I
6.86270 − 1.01696I 0
u = 0.11638 − 1.58430I
a = 0.708844 + 0.840566I
b = −1.010650 − 0.434495I
6.86270 + 1.01696I 0
u = 0.081050 + 0.398783I
a = 0.017573 − 1.190490I
b = −0.626252 + 0.027883I
−0.542904 + 0.116178I −11.65605 − 0.06589I
u = 0.081050 − 0.398783I
a = 0.017573 + 1.190490I
b = −0.626252 − 0.027883I
−0.542904 − 0.116178I −11.65605 + 0.06589I
u = 0.21377 + 1.59894I
a = −0.548072 + 0.656108I
b = 0.831472 − 0.529226I
5.84955 − 6.67507I 0
u = 0.21377 − 1.59894I
a = −0.548072 − 0.656108I
b = 0.831472 + 0.529226I
5.84955 + 6.67507I 0
u = 0.19363 + 1.61491I
a = −0.18710 + 1.43462I
b = −0.179480 − 0.826217I
9.43088 − 5.53156I 0
u = 0.19363 − 1.61491I
a = −0.18710 − 1.43462I
b = −0.179480 + 0.826217I
9.43088 + 5.53156I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25785 + 1.62225I
a = −0.45208 − 1.57984I
b = 1.37064 + 0.34866I
4.54148 − 9.76055I 0
u = 0.25785 − 1.62225I
a = −0.45208 + 1.57984I
b = 1.37064 − 0.34866I
4.54148 + 9.76055I 0
u = 0.26912 + 1.62870I
a = 0.304854 − 1.355430I
b = 0.294539 + 0.827165I
7.56933 − 11.41380I 0
u = 0.26912 − 1.62870I
a = 0.304854 + 1.355430I
b = 0.294539 − 0.827165I
7.56933 + 11.41380I 0
u = 0.31371 + 1.62905I
a = 0.19453 + 1.67286I
b = −1.43525 − 0.33630I
2.0546 − 15.6275I 0
u = 0.31371 − 1.62905I
a = 0.19453 − 1.67286I
b = −1.43525 + 0.33630I
2.0546 + 15.6275I 0
u = 0.261373
a = −2.44078
b = 1.45837
−6.81385 −10.4690
u = 0.198868
a = 1.43681
b = −0.391239
−0.653042 −14.9880
u = −0.0243675 + 0.1369280I
a = −1.13807 + 11.33450I
b = 1.354560 − 0.050472I
−6.43299 + 0.08655I −14.2300 + 0.9460I
u = −0.0243675 − 0.1369280I
a = −1.13807 − 11.33450I
b = 1.354560 + 0.050472I
−6.43299 − 0.08655I −14.2300 − 0.9460I
12
II. I
u
2
= hb
2
− 2, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
u
2
− u + 2
b
a
10
=
1
u
2
a
4
=
u
2
+ b − u + 2
b
a
8
=
−u
2
b + bu − 2b − 1
−2
a
3
=
−u
2
+ u − 2
−b
a
2
=
−u
2
+ u − 2
−b + u
a
7
=
−1
0
a
12
=
u
u
2
− u + 1
a
11
=
u
2
+ 1
u
2
− u + 1
a
6
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u − 24
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
7
c
8
(u
2
− 2)
3
c
6
(u
3
− u
2
+ 1)
2
c
9
, c
10
(u
3
− u
2
+ 2u − 1)
2
c
11
(u
3
+ u
2
− 1)
2
c
12
(u
3
+ u
2
+ 2u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
7
c
8
(y −2)
6
c
6
, c
11
(y
3
− y
2
+ 2y −1)
2
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.122561 − 0.744862I
b = 1.41421
−3.55561 − 2.82812I −16.4902 + 2.9794I
u = 0.215080 + 1.307140I
a = 0.122561 − 0.744862I
b = −1.41421
−3.55561 − 2.82812I −16.4902 + 2.9794I
u = 0.215080 − 1.307140I
a = 0.122561 + 0.744862I
b = 1.41421
−3.55561 + 2.82812I −16.4902 − 2.9794I
u = 0.215080 − 1.307140I
a = 0.122561 + 0.744862I
b = −1.41421
−3.55561 + 2.82812I −16.4902 − 2.9794I
u = 0.569840
a = 1.75488
b = 1.41421
−7.69319 −23.0200
u = 0.569840
a = 1.75488
b = −1.41421
−7.69319 −23.0200
16
III. I
u
3
= hb, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−u
2
+ u − 2
0
a
10
=
1
u
2
a
4
=
−u
2
+ u − 2
0
a
8
=
1
0
a
3
=
−u
2
+ u − 2
0
a
2
=
−u
2
+ u − 2
u
a
7
=
1
0
a
12
=
u
u
2
− u + 1
a
11
=
u
2
+ 1
u
2
− u + 1
a
6
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
+ 2u − 14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
7
c
8
u
3
c
5
(u + 1)
3
c
6
u
3
+ u
2
− 1
c
9
, c
10
u
3
− u
2
+ 2u − 1
c
11
u
3
− u
2
+ 1
c
12
u
3
+ u
2
+ 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
7
c
8
y
3
c
6
, c
11
y
3
− y
2
+ 2y −1
c
9
, c
10
, c
12
y
3
+ 3y
2
+ 2y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = 0
1.37919 − 2.82812I −16.8946 + 3.7388I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = 0
1.37919 + 2.82812I −16.8946 − 3.7388I
u = 0.569840
a = −1.75488
b = 0
−2.75839 −12.2110
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
80
+ 38u
79
+ ··· + 15621u + 529)
c
2
((u − 1)
3
)(u + 1)
6
(u
80
+ 4u
79
+ ··· − 163u − 23)
c
3
, c
4
, c
8
u
3
(u
2
− 2)
3
(u
80
+ u
79
+ ··· − 8u − 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
80
+ 4u
79
+ ··· − 163u − 23)
c
6
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
80
− 2u
79
+ ··· − 4u − 1)
c
7
u
3
(u
2
− 2)
3
(u
80
− 3u
79
+ ··· + 5400u + 1000)
c
9
, c
10
((u
3
− u
2
+ 2u − 1)
3
)(u
80
+ 20u
79
+ ··· + 18u + 1)
c
11
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
80
− 2u
79
+ ··· − 4u − 1)
c
12
((u
3
+ u
2
+ 2u + 1)
3
)(u
80
+ 20u
79
+ ··· + 18u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
80
+ 18y
79
+ ··· − 2.07586 × 10
7
y + 279841)
c
2
, c
5
((y −1)
9
)(y
80
− 38y
79
+ ··· − 15621y + 529)
c
3
, c
4
, c
8
y
3
(y −2)
6
(y
80
− 73y
79
+ ··· + 576y + 64)
c
6
, c
11
((y
3
− y
2
+ 2y −1)
3
)(y
80
− 20y
79
+ ··· − 18y + 1)
c
7
y
3
(y −2)
6
(y
80
+ 11y
79
+ ··· + 9560000y + 1000000)
c
9
, c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
80
+ 84y
79
+ ··· + 86y + 1)
22
