12a
0594
(K12a
0594
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 10 2 12 1 6 5 4 8
Solving Sequence
2,6
7 3
1,10
5 11 9 4 8 12
c
6
c
2
c
1
c
5
c
10
c
9
c
3
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−278579575u
38
+ 801007023u
37
+ ··· + 960147928b + 4668885888,
− 506726616u
38
+ 1536859595u
37
+ ··· + 960147928a + 7944281003, u
39
− 2u
38
+ ··· + 13u − 8i
I
u
2
= h−u
6
+ 2u
4
− u
2
+ b, −u
6
+ u
4
+ a + 1,
u
15
− 5u
13
+ u
12
+ 10u
11
− 4u
10
− 10u
9
+ 6u
8
+ 5u
7
− 5u
6
− u
5
+ 3u
4
+ u
3
− u
2
− u + 1i
I
u
3
= h2b − a + 1, a
2
− 2a + 13, u + 1i
I
u
4
= h2b − a + 1, a
2
− 2a + 5, u − 1i
I
u
5
= hb, a − 1, u + 1i
* 5 irreducible components of dim
C
= 0, with total 59 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−2.79 × 10
8
u
38
+ 8.01 × 10
8
u
37
+ · · · + 9.60 × 10
8
b + 4.67 × 10
9
, −5.07 ×
10
8
u
38
+1.54×10
9
u
37
+· · ·+9.60×10
8
a+7.94×10
9
, u
39
−2u
38
+· · ·+13u−8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
0.527759u
38
− 1.60065u
37
+ ··· + 10.7329u − 8.27402
0.290142u
38
− 0.834254u
37
+ ··· + 7.56410u − 4.86267
a
5
=
0.785150u
38
− 0.610681u
37
+ ··· + 11.4919u − 1.16835
0.354400u
38
− 0.130647u
37
+ ··· + 2.97397u + 2.89166
a
11
=
−0.848153u
38
+ 2.71323u
37
+ ··· − 15.2658u + 5.19809
−0.487224u
38
+ 1.44307u
37
+ ··· − 12.6317u + 7.27384
a
9
=
0.237617u
38
− 0.766395u
37
+ ··· + 3.16882u − 3.41134
0.290142u
38
− 0.834254u
37
+ ··· + 7.56410u − 4.86267
a
4
=
0.150856u
38
+ 0.0217381u
37
+ ··· − 17.3547u + 9.46883
0.170865u
38
− 0.242768u
37
+ ··· − 12.7382u + 5.24191
a
8
=
0.508134u
38
− 1.24630u
37
+ ··· + 5.04688u − 6.94472
0.466487u
38
− 1.22328u
37
+ ··· + 7.11369u − 4.38047
a
12
=
0.546702u
38
− 2.31337u
37
+ ··· + 5.56221u − 1.82639
0.230030u
38
− 1.40951u
37
+ ··· + 12.5505u − 4.06507
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1009740537
480073964
u
38
−
2449057759
480073964
u
37
+ ··· +
13839136571
480073964
u +
1544450212
120018491
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
+ 16u
38
+ ··· + 841u + 64
c
2
, c
6
u
39
− 2u
38
+ ··· + 13u − 8
c
3
u
39
+ 2u
38
+ ··· − 434u − 82
c
4
, c
5
, c
9
c
10
, c
11
u
39
+ 2u
38
+ ··· − 6u − 2
c
7
, c
8
, c
12
u
39
+ 2u
38
+ ··· − 3u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 20y
38
+ ··· + 20945y −4096
c
2
, c
6
y
39
− 16y
38
+ ··· + 841y −64
c
3
y
39
+ 2y
38
+ ··· − 278552y −6724
c
4
, c
5
, c
9
c
10
, c
11
y
39
+ 50y
38
+ ··· + 8y −4
c
7
, c
8
, c
12
y
39
− 40y
38
+ ··· − 535y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.510187 + 0.854260I
a = 0.459599 + 0.050441I
b = −0.601563 − 0.109572I
7.19513 + 1.98650I 12.18743 − 1.52305I
u = 0.510187 − 0.854260I
a = 0.459599 − 0.050441I
b = −0.601563 + 0.109572I
7.19513 − 1.98650I 12.18743 + 1.52305I
u = −0.622477 + 0.793703I
a = 0.715601 − 0.679477I
b = −0.417743 − 0.676425I
5.47691 + 1.45533I 8.53847 − 4.19348I
u = −0.622477 − 0.793703I
a = 0.715601 + 0.679477I
b = −0.417743 + 0.676425I
5.47691 − 1.45533I 8.53847 + 4.19348I
u = 0.340675 + 0.952778I
a = 0.461846 − 1.211810I
b = −0.09622 − 1.69407I
−5.17058 + 7.10896I 5.57947 − 3.18452I
u = 0.340675 − 0.952778I
a = 0.461846 + 1.211810I
b = −0.09622 + 1.69407I
−5.17058 − 7.10896I 5.57947 + 3.18452I
u = −0.409576 + 0.898054I
a = 0.444383 + 0.626707I
b = −0.372437 + 0.928150I
4.02432 − 5.28034I 7.11448 + 4.34651I
u = −0.409576 − 0.898054I
a = 0.444383 − 0.626707I
b = −0.372437 − 0.928150I
4.02432 + 5.28034I 7.11448 − 4.34651I
u = −0.893825 + 0.408631I
a = 0.56327 − 3.33333I
b = 0.02030 − 1.76094I
−12.19790 + 1.67763I 3.69120 − 4.54232I
u = −0.893825 − 0.408631I
a = 0.56327 + 3.33333I
b = 0.02030 + 1.76094I
−12.19790 − 1.67763I 3.69120 + 4.54232I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.880857 + 0.533899I
a = 0.46350 + 1.87403I
b = 0.098417 + 1.194680I
−1.54593 − 2.15130I 4.04314 + 3.05891I
u = 0.880857 − 0.533899I
a = 0.46350 − 1.87403I
b = 0.098417 − 1.194680I
−1.54593 + 2.15130I 4.04314 − 3.05891I
u = −0.892947 + 0.364874I
a = −0.098814 + 0.170736I
b = −0.264285 + 0.451533I
−1.36259 + 1.28896I 1.24891 − 0.92411I
u = −0.892947 − 0.364874I
a = −0.098814 − 0.170736I
b = −0.264285 − 0.451533I
−1.36259 − 1.28896I 1.24891 + 0.92411I
u = 1.073090 + 0.243180I
a = −0.20763 − 1.90178I
b = −0.131098 − 1.030410I
−5.77927 − 0.03027I −4.62865 − 0.08924I
u = 1.073090 − 0.243180I
a = −0.20763 + 1.90178I
b = −0.131098 + 1.030410I
−5.77927 + 0.03027I −4.62865 + 0.08924I
u = 0.980860 + 0.516874I
a = 0.601891 + 0.724041I
b = −0.513688 + 0.161476I
−0.27159 − 4.03311I 6.10073 + 7.35963I
u = 0.980860 − 0.516874I
a = 0.601891 − 0.724041I
b = −0.513688 − 0.161476I
−0.27159 + 4.03311I 6.10073 − 7.35963I
u = 0.807984 + 0.807298I
a = 0.93590 + 1.21554I
b = −0.03886 + 1.59336I
−2.08218 − 2.94056I 6.18654 + 2.75292I
u = 0.807984 − 0.807298I
a = 0.93590 − 1.21554I
b = −0.03886 − 1.59336I
−2.08218 + 2.94056I 6.18654 − 2.75292I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.587388 + 0.621753I
a = −0.417391 − 0.020298I
b = −0.01628 − 1.67009I
−9.77106 − 1.29915I 3.64577 + 3.61671I
u = 0.587388 − 0.621753I
a = −0.417391 + 0.020298I
b = −0.01628 + 1.67009I
−9.77106 + 1.29915I 3.64577 − 3.61671I
u = −1.153580 + 0.222471I
a = −0.20810 + 3.24218I
b = −0.03306 + 1.72517I
−15.6341 − 0.6387I −4.65488 − 0.03706I
u = −1.153580 − 0.222471I
a = −0.20810 − 3.24218I
b = −0.03306 − 1.72517I
−15.6341 + 0.6387I −4.65488 + 0.03706I
u = −1.063930 + 0.555566I
a = 1.47957 − 1.38271I
b = −0.310928 − 0.963275I
−3.72446 + 6.84807I 0.27874 − 7.93372I
u = −1.063930 − 0.555566I
a = 1.47957 + 1.38271I
b = −0.310928 + 0.963275I
−3.72446 − 6.84807I 0.27874 + 7.93372I
u = −1.008430 + 0.658829I
a = 0.103228 − 0.321231I
b = 0.472850 − 0.562157I
4.30632 + 4.00074I 7.24813 − 1.07966I
u = −1.008430 − 0.658829I
a = 0.103228 + 0.321231I
b = 0.472850 + 0.562157I
4.30632 − 4.00074I 7.24813 + 1.07966I
u = 1.115460 + 0.583045I
a = 2.22473 + 2.04920I
b = −0.08101 + 1.70763I
−13.1673 − 8.4053I −0.71469 + 6.01805I
u = 1.115460 − 0.583045I
a = 2.22473 − 2.04920I
b = −0.08101 − 1.70763I
−13.1673 + 8.4053I −0.71469 − 6.01805I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.087820 + 0.664251I
a = −0.350032 − 0.695239I
b = 0.612419 − 0.190625I
5.45311 − 7.62050I 9.27378 + 6.71287I
u = 1.087820 − 0.664251I
a = −0.350032 + 0.695239I
b = 0.612419 + 0.190625I
5.45311 + 7.62050I 9.27378 − 6.71287I
u = −0.623171 + 0.365194I
a = −0.543839 − 0.239201I
b = 0.032741 + 0.707498I
−1.17941 + 1.46032I 3.60067 − 5.27194I
u = −0.623171 − 0.365194I
a = −0.543839 + 0.239201I
b = 0.032741 − 0.707498I
−1.17941 − 1.46032I 3.60067 + 5.27194I
u = −1.146680 + 0.648201I
a = −1.15783 + 1.54546I
b = 0.375338 + 0.995318I
1.80213 + 10.96520I 4.26192 − 8.20321I
u = −1.146680 − 0.648201I
a = −1.15783 − 1.54546I
b = 0.375338 − 0.995318I
1.80213 − 10.96520I 4.26192 + 8.20321I
u = 1.190740 + 0.638471I
a = −1.89201 − 2.31261I
b = 0.10134 − 1.71568I
−7.7538 − 12.8923I 2.81039 + 6.85603I
u = 1.190740 − 0.638471I
a = −1.89201 + 2.31261I
b = 0.10134 + 1.71568I
−7.7538 + 12.8923I 2.81039 − 6.85603I
u = 0.479115
a = −1.28073
b = 0.327545
0.778698 14.3770
8
II. I
u
2
= h−u
6
+ 2u
4
− u
2
+ b, −u
6
+ u
4
+ a + 1, u
15
− 5u
13
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
u
6
− u
4
− 1
u
6
− 2u
4
+ u
2
a
5
=
u
12
− 3u
10
+ 3u
8
− 2u
6
+ 2u
4
− u
2
+ 1
u
12
− 4u
10
+ 6u
8
− 4u
6
+ u
4
a
11
=
−u
13
+ 4u
11
− 5u
9
+ 2u
7
− u
u
12
− 4u
10
+ u
9
+ 6u
8
− 3u
7
− 5u
6
+ 3u
5
+ 3u
4
− u
3
− u
2
+ 1
a
9
=
u
4
− u
2
− 1
u
6
− 2u
4
+ u
2
a
4
=
u
7
− 2u
5
u
9
− 3u
7
+ 3u
5
− 2u
3
+ u
a
8
=
−u
2
− 1
−u
4
a
12
=
−u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
12
− 16u
10
+ 24u
8
− 20u
6
+ 12u
4
− 4u
3
− 4u
2
+ 4u + 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 10u
14
+ ··· + 3u + 1
c
2
, c
6
, c
7
c
8
, c
12
u
15
− 5u
13
+ ··· − u + 1
c
3
(u
5
− u
4
+ u
2
+ u − 1)
3
c
4
, c
5
, c
9
c
10
, c
11
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 10y
14
+ ··· − 9y −1
c
2
, c
6
, c
7
c
8
, c
12
y
15
− 10y
14
+ ··· + 3y −1
c
3
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
3
c
4
, c
5
, c
9
c
10
, c
11
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
3
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.906686 + 0.468417I
a = −1.72729 + 0.71115I
b = 0.233677 + 0.885557I
−1.81981 + 2.21397I 3.11432 − 4.22289I
u = −0.906686 − 0.468417I
a = −1.72729 − 0.71115I
b = 0.233677 − 0.885557I
−1.81981 − 2.21397I 3.11432 + 4.22289I
u = 0.989359 + 0.555107I
a = −2.36917 − 1.31631I
b = 0.05818 − 1.69128I
−10.95830 − 3.33174I 2.08126 + 2.36228I
u = 0.989359 − 0.555107I
a = −2.36917 + 1.31631I
b = 0.05818 + 1.69128I
−10.95830 + 3.33174I 2.08126 − 2.36228I
u = 0.359454 + 0.759797I
a = −0.591315 + 0.655548I
b = 0.05818 + 1.69128I
−10.95830 + 3.33174I 2.08126 − 2.36228I
u = 0.359454 − 0.759797I
a = −0.591315 − 0.655548I
b = 0.05818 − 1.69128I
−10.95830 − 3.33174I 2.08126 + 2.36228I
u = −1.23403
a = 0.212482
b = 0.416284
0.882183 11.6090
u = −0.379822 + 0.616522I
a = −0.694211 − 0.196319I
b = 0.233677 − 0.885557I
−1.81981 − 2.21397I 3.11432 + 4.22289I
u = −0.379822 − 0.616522I
a = −0.694211 + 0.196319I
b = 0.233677 + 0.885557I
−1.81981 + 2.21397I 3.11432 − 4.22289I
u = 0.617017 + 0.377000I
a = −0.981816 − 0.243241I
b = 0.416284
0.882183 11.60884 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617017 − 0.377000I
a = −0.981816 + 0.243241I
b = 0.416284
0.882183 11.60884 + 0.I
u = 1.286510 + 0.148105I
a = 0.12253 + 1.74921I
b = 0.233677 + 0.885557I
−1.81981 + 2.21397I 3.11432 − 4.22289I
u = 1.286510 − 0.148105I
a = 0.12253 − 1.74921I
b = 0.233677 − 0.885557I
−1.81981 − 2.21397I 3.11432 + 4.22289I
u = −1.348810 + 0.204690I
a = 0.13503 − 3.10198I
b = 0.05818 − 1.69128I
−10.95830 − 3.33174I 2.08126 + 2.36228I
u = −1.348810 − 0.204690I
a = 0.13503 + 3.10198I
b = 0.05818 + 1.69128I
−10.95830 + 3.33174I 2.08126 − 2.36228I
13
III. I
u
3
= h2b − a + 1, a
2
− 2a + 13, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
1
=
−1
−1
a
10
=
a
1
2
a −
1
2
a
5
=
1
2
a −
11
2
−3
a
11
=
−
3
2
a −
1
2
−a + 1
a
9
=
1
2
a +
1
2
1
2
a −
1
2
a
4
=
−
1
2
a +
9
2
3
a
8
=
1
2
a +
3
2
1
2
a +
1
2
a
12
=
1
2
a +
1
2
1
2
a −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
2
+ 3
c
6
, c
7
, c
8
(u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y −1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y + 3)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000 + 3.46410I
b = 1.73205I
−13.1595 0
u = −1.00000
a = 1.00000 − 3.46410I
b = − 1.73205I
−13.1595 0
17
IV. I
u
4
= h2b − a + 1, a
2
− 2a + 5, u − 1i
(i) Arc colorings
a
2
=
0
1
a
6
=
1
0
a
7
=
1
1
a
3
=
−1
0
a
1
=
1
1
a
10
=
a
1
2
a −
1
2
a
5
=
1
2
a −
3
2
−1
a
11
=
1
2
a −
1
2
0
a
9
=
1
2
a +
1
2
1
2
a −
1
2
a
4
=
1
2
a −
5
2
−1
a
8
=
1
2
a +
3
2
1
2
a +
1
2
a
12
=
−
1
2
a −
1
2
−
1
2
a +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
8
(u − 1)
2
c
2
, c
12
(u + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y −1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000 + 2.00000I
b = 1.000000I
−3.28987 0
u = 1.00000
a = 1.00000 − 2.00000I
b = − 1.000000I
−3.28987 0
21
V. I
u
5
= hb, a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
1
=
−1
−1
a
10
=
1
0
a
5
=
1
0
a
11
=
1
0
a
9
=
1
0
a
4
=
1
0
a
8
=
2
1
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
7
, c
8
u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y −1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
0 0
25
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
15
+ 10u
14
+ ··· + 3u + 1)(u
39
+ 16u
38
+ ··· + 841u + 64)
c
2
((u − 1)
3
)(u + 1)
2
(u
15
− 5u
13
+ ··· − u + 1)(u
39
− 2u
38
+ ··· + 13u − 8)
c
3
u(u
2
+ 1)(u
2
+ 3)(u
5
− u
4
+ ··· + u − 1)
3
(u
39
+ 2u
38
+ ··· − 434u − 82)
c
4
, c
5
, c
9
c
10
, c
11
u(u
2
+ 1)(u
2
+ 3)(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
3
· (u
39
+ 2u
38
+ ··· − 6u − 2)
c
6
((u − 1)
2
)(u + 1)
3
(u
15
− 5u
13
+ ··· − u + 1)(u
39
− 2u
38
+ ··· + 13u − 8)
c
7
, c
8
((u − 1)
2
)(u + 1)
3
(u
15
− 5u
13
+ ··· − u + 1)(u
39
+ 2u
38
+ ··· − 3u − 8)
c
12
((u − 1)
3
)(u + 1)
2
(u
15
− 5u
13
+ ··· − u + 1)(u
39
+ 2u
38
+ ··· − 3u − 8)
26
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
15
− 10y
14
+ ··· − 9y −1)
· (y
39
+ 20y
38
+ ··· + 20945y −4096)
c
2
, c
6
((y −1)
5
)(y
15
− 10y
14
+ ··· + 3y −1)(y
39
− 16y
38
+ ··· + 841y −64)
c
3
y(y + 1)
2
(y + 3)
2
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
3
· (y
39
+ 2y
38
+ ··· − 278552y −6724)
c
4
, c
5
, c
9
c
10
, c
11
y(y + 1)
2
(y + 3)
2
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
3
· (y
39
+ 50y
38
+ ··· + 8y −4)
c
7
, c
8
, c
12
((y −1)
5
)(y
15
− 10y
14
+ ··· + 3y −1)(y
39
− 40y
38
+ ··· − 535y −64)
27
