12a
0356
(K12a
0356
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 11 5 4 1 12 7 10
Solving Sequence
6,11
7
3,12
2 1 5 8 4 10 9
c
6
c
11
c
2
c
1
c
5
c
7
c
4
c
10
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.66231 × 10
18
u
58
+ 4.32374 × 10
18
u
57
+ ··· + 8.19653 × 10
18
b + 1.17819 × 10
19
,
7.79962 × 10
19
u
58
− 1.20924 × 10
20
u
57
+ ··· + 4.91792 × 10
19
a − 4.08773 × 10
20
, u
59
− 2u
58
+ ··· + u + 3i
I
u
2
= hb − 1, a
2
+ 2au + 3u
2
− 2a − 6u + 3, u
3
− u
2
+ 1i
I
u
3
= hb + 1, a + u + 1, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 68 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−5.66×10
18
u
58
+4.32×10
18
u
57
+· · ·+8.20×10
18
b+1.18×10
19
, 7.80×
10
19
u
58
−1.21×10
20
u
57
+· · ·+4.92×10
19
a−4.09×10
20
, u
59
−2u
58
+· · ·+u+3i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
−1.58596u
58
+ 2.45885u
57
+ ··· + 9.55113u + 8.31191
0.690818u
58
− 0.527509u
57
+ ··· − 0.607836u − 1.43742
a
12
=
−u
−u
3
+ u
a
2
=
−0.895140u
58
+ 1.93134u
57
+ ··· + 8.94330u + 6.87449
0.690818u
58
− 0.527509u
57
+ ··· − 0.607836u − 1.43742
a
1
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
5
=
1.92952u
58
− 2.67059u
57
+ ··· − 12.7404u − 7.85154
−0.222016u
58
− 0.0475838u
57
+ ··· + 0.650562u − 0.281439
a
8
=
1.18721u
58
− 1.74998u
57
+ ··· + 3.24272u + 0.910386
0.412864u
58
− 0.942970u
57
+ ··· − 5.73768u − 1.86980
a
4
=
−1.56955u
58
+ 2.85972u
57
+ ··· + 12.4812u + 9.51305
0.495410u
58
− 0.282318u
57
+ ··· + 1.25035u − 0.561736
a
10
=
u
3
u
5
− u
3
+ u
a
9
=
u
7
+ 2u
3
u
9
− u
7
+ 3u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
23751865828353822111
8196531629884877029
u
58
−
18808285269894389520
8196531629884877029
u
57
+ ··· −
86244640466854553084
8196531629884877029
u −
226494452198725358175
8196531629884877029
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
+ 24u
58
+ ··· − 32u + 1
c
2
, c
5
u
59
+ 4u
58
+ ··· − 4u + 1
c
3
, c
4
, c
7
c
8
u
59
− u
58
+ ··· + 64u
2
+ 8
c
6
, c
11
u
59
− 2u
58
+ ··· + u + 3
c
9
, c
10
, c
12
u
59
+ 14u
58
+ ··· + 157u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
+ 32y
58
+ ··· − 1936y −1
c
2
, c
5
y
59
− 24y
58
+ ··· − 32y −1
c
3
, c
4
, c
7
c
8
y
59
+ 73y
58
+ ··· − 1024y −64
c
6
, c
11
y
59
− 14y
58
+ ··· + 157y −9
c
9
, c
10
, c
12
y
59
+ 66y
58
+ ··· − 1307y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950749 + 0.085534I
a = 1.40102 + 0.37767I
b = 0.881025 + 0.388729I
−2.20168 − 1.55351I −13.9942 + 4.5761I
u = −0.950749 − 0.085534I
a = 1.40102 − 0.37767I
b = 0.881025 − 0.388729I
−2.20168 + 1.55351I −13.9942 − 4.5761I
u = 0.955755 + 0.424887I
a = 1.39192 − 1.56772I
b = 1.001090 + 0.566158I
−0.26151 − 6.93624I −11.4611 + 10.0156I
u = 0.955755 − 0.424887I
a = 1.39192 + 1.56772I
b = 1.001090 − 0.566158I
−0.26151 + 6.93624I −11.4611 − 10.0156I
u = 1.061230 + 0.059722I
a = −1.249430 + 0.518825I
b = −0.871450 + 0.680013I
5.44848 + 2.62573I −10.72193 − 2.36500I
u = 1.061230 − 0.059722I
a = −1.249430 − 0.518825I
b = −0.871450 − 0.680013I
5.44848 − 2.62573I −10.72193 + 2.36500I
u = 0.808456 + 0.470326I
a = −0.499696 − 0.009506I
b = 0.399158 − 0.576724I
1.30057 − 2.44037I −6.97566 + 5.43591I
u = 0.808456 − 0.470326I
a = −0.499696 + 0.009506I
b = 0.399158 + 0.576724I
1.30057 + 2.44037I −6.97566 − 5.43591I
u = −0.841496 + 0.395242I
a = −0.96036 − 2.04635I
b = −0.942517 + 0.431284I
−1.79109 + 3.29910I −14.9386 − 5.3714I
u = −0.841496 − 0.395242I
a = −0.96036 + 2.04635I
b = −0.942517 − 0.431284I
−1.79109 − 3.29910I −14.9386 + 5.3714I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428912 + 0.779191I
a = 0.069578 − 1.101110I
b = −0.759172 + 0.857390I
10.95100 + 1.36331I −3.49056 − 2.36160I
u = −0.428912 − 0.779191I
a = 0.069578 + 1.101110I
b = −0.759172 − 0.857390I
10.95100 − 1.36331I −3.49056 + 2.36160I
u = −1.039320 + 0.443029I
a = −1.56082 − 1.25858I
b = −1.062320 + 0.707142I
7.76213 + 9.14001I −12.0000 − 7.5958I
u = −1.039320 − 0.443029I
a = −1.56082 + 1.25858I
b = −1.062320 − 0.707142I
7.76213 − 9.14001I −12.0000 + 7.5958I
u = 0.883608 + 0.704164I
a = 0.236690 − 0.559685I
b = 0.746146 − 0.071860I
1.94353 − 2.69934I 0
u = 0.883608 − 0.704164I
a = 0.236690 + 0.559685I
b = 0.746146 + 0.071860I
1.94353 + 2.69934I 0
u = −0.995779 + 0.541016I
a = 0.394659 − 0.390928I
b = −0.608688 − 0.798203I
9.11589 + 3.43180I −12.00000 + 0.I
u = −0.995779 − 0.541016I
a = 0.394659 + 0.390928I
b = −0.608688 + 0.798203I
9.11589 − 3.43180I −12.00000 + 0.I
u = −0.865723 + 0.753965I
a = −0.987861 + 0.232003I
b = 0.0644711 − 0.1218690I
7.97460 + 2.84682I 0
u = −0.865723 − 0.753965I
a = −0.987861 − 0.232003I
b = 0.0644711 + 0.1218690I
7.97460 − 2.84682I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.287017 + 0.779308I
a = 0.328056 + 0.939299I
b = −0.992597 − 0.783531I
10.23980 − 4.73907I −4.25165 + 2.78795I
u = −0.287017 − 0.779308I
a = 0.328056 − 0.939299I
b = −0.992597 + 0.783531I
10.23980 + 4.73907I −4.25165 − 2.78795I
u = −0.718782 + 0.401065I
a = 1.86408 + 0.41857I
b = 1.231790 + 0.111942I
3.40228 + 1.59157I −9.70315 − 4.05404I
u = −0.718782 − 0.401065I
a = 1.86408 − 0.41857I
b = 1.231790 − 0.111942I
3.40228 − 1.59157I −9.70315 + 4.05404I
u = 0.779291 + 0.186002I
a = −1.76043 + 0.35358I
b = −1.092770 + 0.150850I
−2.95013 − 0.58618I −15.2527 + 9.8012I
u = 0.779291 − 0.186002I
a = −1.76043 − 0.35358I
b = −1.092770 − 0.150850I
−2.95013 + 0.58618I −15.2527 − 9.8012I
u = −0.893562 + 0.803723I
a = −0.002799 − 0.814217I
b = −1.251010 − 0.015615I
2.63289 + 3.01191I 0
u = −0.893562 − 0.803723I
a = −0.002799 + 0.814217I
b = −1.251010 + 0.015615I
2.63289 − 3.01191I 0
u = −0.854945 + 0.893449I
a = −0.723640 − 1.049790I
b = 1.036460 + 0.751160I
8.28053 − 4.23254I 0
u = −0.854945 − 0.893449I
a = −0.723640 + 1.049790I
b = 1.036460 − 0.751160I
8.28053 + 4.23254I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886324 + 0.866549I
a = 0.98642 − 1.06679I
b = −0.845945 + 0.735665I
5.94223 − 0.39886I 0
u = 0.886324 − 0.866549I
a = 0.98642 + 1.06679I
b = −0.845945 − 0.735665I
5.94223 + 0.39886I 0
u = 0.832835 + 0.926311I
a = 0.571242 − 0.903844I
b = −1.18749 + 0.79875I
16.9600 + 7.2294I 0
u = 0.832835 − 0.926311I
a = 0.571242 + 0.903844I
b = −1.18749 − 0.79875I
16.9600 − 7.2294I 0
u = −0.897663 + 0.871706I
a = −0.13642 + 1.69360I
b = 0.673711 − 0.844140I
9.36550 + 1.73164I 0
u = −0.897663 − 0.871706I
a = −0.13642 − 1.69360I
b = 0.673711 + 0.844140I
9.36550 − 1.73164I 0
u = 0.915394 + 0.861826I
a = −0.067431 − 0.859114I
b = 1.48127 − 0.02057I
10.78160 − 3.19575I 0
u = 0.915394 − 0.861826I
a = −0.067431 + 0.859114I
b = 1.48127 + 0.02057I
10.78160 + 3.19575I 0
u = 0.938182 + 0.846227I
a = 0.00707 + 2.10628I
b = −0.898285 − 0.723052I
5.77879 − 5.95695I 0
u = 0.938182 − 0.846227I
a = 0.00707 − 2.10628I
b = −0.898285 + 0.723052I
5.77879 + 5.95695I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933873 + 0.857641I
a = −1.114390 − 0.849709I
b = 0.624353 + 0.869336I
9.25182 + 4.67664I 0
u = −0.933873 − 0.857641I
a = −1.114390 + 0.849709I
b = 0.624353 − 0.869336I
9.25182 − 4.67664I 0
u = 0.875079 + 0.923683I
a = −0.06377 + 1.45605I
b = −0.571370 − 1.103440I
18.8901 + 0.4011I 0
u = 0.875079 − 0.923683I
a = −0.06377 − 1.45605I
b = −0.571370 + 1.103440I
18.8901 − 0.4011I 0
u = 0.469446 + 0.544141I
a = −0.223809 − 1.235640I
b = 0.654076 + 0.529004I
2.26071 − 1.37979I −4.27858 + 3.91647I
u = 0.469446 − 0.544141I
a = −0.223809 + 1.235640I
b = 0.654076 − 0.529004I
2.26071 + 1.37979I −4.27858 − 3.91647I
u = 0.667363 + 0.266454I
a = −0.70482 − 2.96122I
b = 0.852790 + 0.242476I
2.81040 − 1.03770I −8.02636 + 6.84259I
u = 0.667363 − 0.266454I
a = −0.70482 + 2.96122I
b = 0.852790 − 0.242476I
2.81040 + 1.03770I −8.02636 − 6.84259I
u = −0.972360 + 0.842990I
a = 0.31648 + 2.17743I
b = 1.070130 − 0.736498I
7.90798 + 10.65770I 0
u = −0.972360 − 0.842990I
a = 0.31648 − 2.17743I
b = 1.070130 + 0.736498I
7.90798 − 10.65770I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.312980 + 0.623983I
a = −0.499965 + 1.002160I
b = 0.872314 − 0.581880I
1.73082 + 3.05513I −5.72428 − 4.49353I
u = 0.312980 − 0.623983I
a = −0.499965 − 1.002160I
b = 0.872314 + 0.581880I
1.73082 − 3.05513I −5.72428 + 4.49353I
u = 1.002690 + 0.845529I
a = −0.53525 + 2.09749I
b = −1.20584 − 0.77319I
16.4153 − 13.7600I 0
u = 1.002690 − 0.845529I
a = −0.53525 − 2.09749I
b = −1.20584 + 0.77319I
16.4153 + 13.7600I 0
u = 0.980128 + 0.871697I
a = 1.090820 − 0.722028I
b = −0.524644 + 1.106680I
18.5511 − 7.0143I 0
u = 0.980128 − 0.871697I
a = 1.090820 + 0.722028I
b = −0.524644 − 1.106680I
18.5511 + 7.0143I 0
u = −0.450920 + 0.353539I
a = 1.152780 + 0.540477I
b = −0.620312 − 0.297342I
−0.634650 − 0.118465I −11.69433 − 0.33232I
u = −0.450920 − 0.353539I
a = 1.152780 − 0.540477I
b = −0.620312 + 0.297342I
−0.634650 + 0.118465I −11.69433 + 0.33232I
u = −0.475308
a = 0.893509
b = −0.308761
−0.673099 −14.6220
10
II. I
u
2
= hb − 1, a
2
+ 2au + 3u
2
− 2a − 6u + 3, u
3
− u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
a
1
a
12
=
−u
−u
2
+ u + 1
a
2
=
a + 1
1
a
1
=
1
0
a
5
=
−a
−1
a
8
=
−a − 3u + 4
−u
2
a + u
2
+ 1
a
4
=
u
2
a + a − 1
u
2
a − au − u
2
− a + 1
a
10
=
u
2
− 1
−u
2
a
9
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 12
11
(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
12
(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
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 1.175960 − 0.571534I
b = 1.00000
6.31400 − 2.82812I −8.49024 + 2.97945I
u = 0.877439 + 0.744862I
a = −0.930832 − 0.918189I
b = 1.00000
6.31400 − 2.82812I −8.49024 + 2.97945I
u = 0.877439 − 0.744862I
a = 1.175960 + 0.571534I
b = 1.00000
6.31400 + 2.82812I −8.49024 − 2.97945I
u = 0.877439 − 0.744862I
a = −0.930832 + 0.918189I
b = 1.00000
6.31400 + 2.82812I −8.49024 − 2.97945I
u = −0.754878
a = 1.75488 + 2.48177I
b = 1.00000
2.17641 −15.0200
u = −0.754878
a = 1.75488 − 2.48177I
b = 1.00000
2.17641 −15.0200
14
III. I
u
3
= hb + 1, a + u + 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
−u − 1
−1
a
12
=
−u
u
2
+ u − 1
a
2
=
−u − 2
−1
a
1
=
−1
0
a
5
=
−u − 1
−1
a
8
=
1
u
2
a
4
=
−u − 1
−1
a
10
=
−u
2
+ 1
u
2
a
9
=
1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 2u − 16
15
(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
16
(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
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.122561 − 0.744862I
b = −1.00000
1.37919 + 2.82812I −16.8946 − 3.7388I
u = −0.877439 − 0.744862I
a = −0.122561 + 0.744862I
b = −1.00000
1.37919 − 2.82812I −16.8946 + 3.7388I
u = 0.754878
a = −1.75488
b = −1.00000
−2.75839 −12.2110
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
59
+ 24u
58
+ ··· − 32u + 1)
c
2
((u − 1)
3
)(u + 1)
6
(u
59
+ 4u
58
+ ··· − 4u + 1)
c
3
, c
4
, c
7
c
8
u
3
(u
2
+ 2)
3
(u
59
− u
58
+ ··· + 64u
2
+ 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
59
+ 4u
58
+ ··· − 4u + 1)
c
6
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
59
− 2u
58
+ ··· + u + 3)
c
9
, c
10
((u
3
− u
2
+ 2u − 1)
3
)(u
59
+ 14u
58
+ ··· + 157u + 9)
c
11
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
59
− 2u
58
+ ··· + u + 3)
c
12
((u
3
+ u
2
+ 2u + 1)
3
)(u
59
+ 14u
58
+ ··· + 157u + 9)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
59
+ 32y
58
+ ··· − 1936y −1)
c
2
, c
5
((y −1)
9
)(y
59
− 24y
58
+ ··· − 32y −1)
c
3
, c
4
, c
7
c
8
y
3
(y + 2)
6
(y
59
+ 73y
58
+ ··· − 1024y −64)
c
6
, c
11
((y
3
− y
2
+ 2y −1)
3
)(y
59
− 14y
58
+ ··· + 157y −9)
c
9
, c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
59
+ 66y
58
+ ··· − 1307y −81)
20
