12a
0676
(K12a
0676
)
A knot diagram
1
Linearized knot diagam
3 7 11 10 8 2 6 5 12 1 9 4
Solving Sequence
2,6
7
3,11
4 8 1 5 9 10 12
c
6
c
2
c
3
c
7
c
1
c
5
c
8
c
10
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.44258 × 10
23
u
71
+ 3.59914 × 10
23
u
70
+ ··· + 7.89345 × 10
22
b − 2.68405 × 10
23
,
− 1.39901 × 10
23
u
71
+ 3.60918 × 10
23
u
70
+ ··· + 7.89345 × 10
22
a + 4.78490 × 10
22
, u
72
− 2u
71
+ ··· + 3u + 1i
I
u
2
= hb − u + 1, u
2
+ a − u, u
3
− u
2
+ 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
= h−1.44×10
23
u
71
+3.60×10
23
u
70
+· · ·+7.89×10
22
b−2.68×10
23
, −1.40×
10
23
u
71
+3.61×10
23
u
70
+· · ·+7.89×10
22
a+4.78×10
22
, u
72
−2u
71
+· · ·+3u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
1.77237u
71
− 4.57237u
70
+ ··· + 0.769849u − 0.606185
1.82757u
71
− 4.55965u
70
+ ··· + 9.83520u + 3.40035
a
4
=
−4.80003u
71
+ 11.7741u
70
+ ··· − 2.80818u − 4.87175
−5.18354u
71
+ 14.7695u
70
+ ··· − 9.65757u − 7.77645
a
8
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
4
− u
2
+ 1
−u
4
a
9
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
10
=
1.73698u
71
− 4.53698u
70
+ ··· + 1.12293u − 0.488491
1.86225u
71
− 4.76003u
70
+ ··· + 9.75138u + 3.39997
a
12
=
1.80708u
71
− 4.60708u
70
+ ··· − 0.0706153u + 0.176461
1.99306u
71
− 4.95992u
70
+ ··· + 10.2168u + 3.60008
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3029559155238658290078361
78934523837018836771529
u
71
−
8171406099798322196390615
78934523837018836771529
u
70
+ ··· +
4343268651222967960133360
78934523837018836771529
u +
3408340608627538586838312
78934523837018836771529
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
8
u
72
+ 14u
71
+ ··· + u + 1
c
2
, c
6
u
72
− 2u
71
+ ··· + 3u + 1
c
3
u
72
− 3u
71
+ ··· − 164u − 53
c
4
u
72
− 5u
71
+ ··· − 32u + 1
c
9
, c
11
u
72
− 4u
71
+ ··· + 2u − 1
c
10
u
72
+ 11u
71
+ ··· − 4u + 8
c
12
u
72
+ 4u
71
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
8
y
72
+ 90y
71
+ ··· + 123y + 1
c
2
, c
6
y
72
− 14y
71
+ ··· − y + 1
c
3
y
72
− 79y
71
+ ··· + 38824y + 2809
c
4
y
72
− 59y
71
+ ··· − 416y + 1
c
9
, c
11
y
72
− 40y
71
+ ··· − 82y + 1
c
10
y
72
− 21y
71
+ ··· − 1872y + 64
c
12
y
72
+ 14y
71
+ ··· − y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968902 + 0.264227I
a = −0.466064 − 0.401865I
b = 0.589810 − 0.192391I
−3.89955 − 2.26043I 0
u = −0.968902 − 0.264227I
a = −0.466064 + 0.401865I
b = 0.589810 + 0.192391I
−3.89955 + 2.26043I 0
u = −0.837009 + 0.531428I
a = −1.79640 + 0.60404I
b = 1.53021 + 0.76581I
−1.45829 + 5.16912I 0
u = −0.837009 − 0.531428I
a = −1.79640 − 0.60404I
b = 1.53021 − 0.76581I
−1.45829 − 5.16912I 0
u = 0.963527 + 0.168807I
a = −0.205175 − 0.227411I
b = −0.609188 + 1.049750I
−4.41858 − 7.88528I 0
u = 0.963527 − 0.168807I
a = −0.205175 + 0.227411I
b = −0.609188 − 1.049750I
−4.41858 + 7.88528I 0
u = 0.801619 + 0.650298I
a = −0.1235270 + 0.0608340I
b = 0.362049 + 0.280836I
2.44196 − 2.47078I 0
u = 0.801619 − 0.650298I
a = −0.1235270 − 0.0608340I
b = 0.362049 − 0.280836I
2.44196 + 2.47078I 0
u = 0.788074 + 0.561663I
a = −2.63792 − 1.76345I
b = 1.021010 + 0.526040I
0.09175 − 2.64810I 0. − 12.56607I
u = 0.788074 − 0.561663I
a = −2.63792 + 1.76345I
b = 1.021010 − 0.526040I
0.09175 + 2.64810I 0. + 12.56607I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672578 + 0.792936I
a = 0.823148 − 0.340327I
b = −0.323921 + 0.762920I
2.70900 − 3.15094I 0
u = 0.672578 − 0.792936I
a = 0.823148 + 0.340327I
b = −0.323921 − 0.762920I
2.70900 + 3.15094I 0
u = −0.936556
a = −0.0800858
b = −0.822255
−1.61727 −3.00800
u = −0.882133 + 0.595412I
a = −0.77420 + 1.19520I
b = 1.43975 − 0.95089I
3.44838 + 7.01000I 0
u = −0.882133 − 0.595412I
a = −0.77420 − 1.19520I
b = 1.43975 + 0.95089I
3.44838 − 7.01000I 0
u = −0.627065 + 0.693340I
a = 1.62692 − 0.65486I
b = −1.091230 − 0.419584I
4.28127 − 2.21641I 0
u = −0.627065 − 0.693340I
a = 1.62692 + 0.65486I
b = −1.091230 + 0.419584I
4.28127 + 2.21641I 0
u = −0.542743 + 0.760330I
a = −1.35987 + 0.89996I
b = 0.950096 − 0.498703I
1.26807 − 7.90640I 0. + 4.88275I
u = −0.542743 − 0.760330I
a = −1.35987 − 0.89996I
b = 0.950096 + 0.498703I
1.26807 + 7.90640I 0. − 4.88275I
u = 0.707463 + 0.576385I
a = 1.82821 + 1.70583I
b = −1.14473 − 1.52935I
0.35169 − 1.67874I −8.0346 + 12.5584I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707463 − 0.576385I
a = 1.82821 − 1.70583I
b = −1.14473 + 1.52935I
0.35169 + 1.67874I −8.0346 − 12.5584I
u = 0.950289 + 0.528900I
a = 0.496182 + 0.879142I
b = −0.380086 − 0.410207I
1.51382 − 5.03623I 0
u = 0.950289 − 0.528900I
a = 0.496182 − 0.879142I
b = −0.380086 + 0.410207I
1.51382 + 5.03623I 0
u = −0.765809 + 0.473153I
a = −0.559849 − 0.130249I
b = −0.46632 + 1.52805I
−2.54645 + 1.81480I −11.24770 − 4.52021I
u = −0.765809 − 0.473153I
a = −0.559849 + 0.130249I
b = −0.46632 − 1.52805I
−2.54645 − 1.81480I −11.24770 + 4.52021I
u = −0.953950 + 0.579297I
a = 1.28886 − 0.88100I
b = −1.122300 + 0.316177I
−0.08677 + 12.83750I 0
u = −0.953950 − 0.579297I
a = 1.28886 + 0.88100I
b = −1.122300 − 0.316177I
−0.08677 − 12.83750I 0
u = 0.499560 + 0.694540I
a = −1.201160 + 0.065538I
b = 0.709959 + 0.050244I
2.97800 + 0.47203I 1.72924 − 1.55020I
u = 0.499560 − 0.694540I
a = −1.201160 − 0.065538I
b = 0.709959 − 0.050244I
2.97800 − 0.47203I 1.72924 + 1.55020I
u = 0.813920 + 0.197808I
a = 0.003055 + 0.917148I
b = 0.323912 − 1.127260I
−0.75535 − 3.39687I −8.26248 + 8.56994I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.813920 − 0.197808I
a = 0.003055 − 0.917148I
b = 0.323912 + 1.127260I
−0.75535 + 3.39687I −8.26248 − 8.56994I
u = −0.615151 + 0.551675I
a = 0.53717 − 1.60738I
b = −1.37830 + 0.97742I
−0.763729 − 1.003110I −6.06520 + 2.84230I
u = −0.615151 − 0.551675I
a = 0.53717 + 1.60738I
b = −1.37830 − 0.97742I
−0.763729 + 1.003110I −6.06520 − 2.84230I
u = 0.953441 + 0.705802I
a = 0.359518 − 0.560462I
b = 0.232048 + 0.838202I
1.86961 − 2.36944I 0
u = 0.953441 − 0.705802I
a = 0.359518 + 0.560462I
b = 0.232048 − 0.838202I
1.86961 + 2.36944I 0
u = 0.798195 + 0.054269I
a = 1.44619 + 0.40925I
b = −0.451145 − 1.014630I
−4.41829 − 1.60184I −17.9572 + 4.5768I
u = 0.798195 − 0.054269I
a = 1.44619 − 0.40925I
b = −0.451145 + 1.014630I
−4.41829 + 1.60184I −17.9572 − 4.5768I
u = −0.715143 + 0.104849I
a = −0.120961 − 0.148988I
b = −0.713601 + 0.443948I
−1.135390 + 0.150760I −9.68659 − 0.82277I
u = −0.715143 − 0.104849I
a = −0.120961 + 0.148988I
b = −0.713601 − 0.443948I
−1.135390 − 0.150760I −9.68659 + 0.82277I
u = −0.887595 + 0.926385I
a = 1.62680 − 1.07259I
b = −2.66969 − 0.98983I
11.21660 − 1.64667I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.887595 − 0.926385I
a = 1.62680 + 1.07259I
b = −2.66969 + 0.98983I
11.21660 + 1.64667I 0
u = 0.927711 + 0.887451I
a = −0.186364 + 0.276748I
b = 0.457548 + 0.191821I
5.73987 − 3.27877I 0
u = 0.927711 − 0.887451I
a = −0.186364 − 0.276748I
b = 0.457548 − 0.191821I
5.73987 + 3.27877I 0
u = 0.915139 + 0.900867I
a = −1.07202 − 1.74600I
b = 3.62389 + 0.18229I
7.54879 + 0.58276I 0
u = 0.915139 − 0.900867I
a = −1.07202 + 1.74600I
b = 3.62389 − 0.18229I
7.54879 − 0.58276I 0
u = −0.926626 + 0.902491I
a = −3.29968 + 2.23419I
b = 5.82902 + 1.51753I
9.16836 + 2.49320I 0
u = −0.926626 − 0.902491I
a = −3.29968 − 2.23419I
b = 5.82902 − 1.51753I
9.16836 − 2.49320I 0
u = 0.894832 + 0.934493I
a = 1.47190 + 2.10489I
b = −3.70581 − 0.00429I
10.06680 + 9.25135I 0
u = 0.894832 − 0.934493I
a = 1.47190 − 2.10489I
b = −3.70581 + 0.00429I
10.06680 − 9.25135I 0
u = 0.945151 + 0.886788I
a = 1.82993 + 1.05340I
b = −3.14838 + 1.79988I
7.45245 − 7.18019I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.945151 − 0.886788I
a = 1.82993 − 1.05340I
b = −3.14838 − 1.79988I
7.45245 + 7.18019I 0
u = 0.912379 + 0.922074I
a = −1.44227 − 1.52272I
b = 2.92179 − 0.80824I
13.33720 + 2.59179I 0
u = 0.912379 − 0.922074I
a = −1.44227 + 1.52272I
b = 2.92179 + 0.80824I
13.33720 − 2.59179I 0
u = −0.939518 + 0.896155I
a = 2.45229 − 3.28599I
b = −5.86565 − 0.05755I
9.12667 + 4.14015I 0
u = −0.939518 − 0.896155I
a = 2.45229 + 3.28599I
b = −5.86565 + 0.05755I
9.12667 − 4.14015I 0
u = −0.925097 + 0.928051I
a = −0.668220 + 0.883655I
b = 1.44462 + 0.22158I
12.70380 + 2.76882I 0
u = −0.925097 − 0.928051I
a = −0.668220 − 0.883655I
b = 1.44462 − 0.22158I
12.70380 − 2.76882I 0
u = −0.687552
a = 2.99846
b = 4.14675
−2.65408 94.5990
u = 0.961864 + 0.896115I
a = 1.53307 + 1.32987I
b = −3.56486 + 0.38651I
13.1756 − 9.2867I 0
u = 0.961864 − 0.896115I
a = 1.53307 − 1.32987I
b = −3.56486 − 0.38651I
13.1756 + 9.2867I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.977744 + 0.880445I
a = −1.17212 + 1.51469I
b = 3.05247 − 0.03420I
10.92380 + 8.30184I 0
u = −0.977744 − 0.880445I
a = −1.17212 − 1.51469I
b = 3.05247 + 0.03420I
10.92380 − 8.30184I 0
u = −0.073283 + 0.676263I
a = 0.247487 − 0.921014I
b = 0.369400 − 0.069244I
−0.94073 + 5.37603I −2.50022 − 5.98273I
u = −0.073283 − 0.676263I
a = 0.247487 + 0.921014I
b = 0.369400 + 0.069244I
−0.94073 − 5.37603I −2.50022 + 5.98273I
u = −0.959256 + 0.908713I
a = 0.921830 − 0.524750I
b = −1.75197 − 0.38856I
12.59070 + 3.98684I 0
u = −0.959256 − 0.908713I
a = 0.921830 + 0.524750I
b = −1.75197 + 0.38856I
12.59070 − 3.98684I 0
u = 0.979452 + 0.889436I
a = −2.17771 − 1.34335I
b = 3.93843 − 1.30440I
9.7900 − 15.9619I 0
u = 0.979452 − 0.889436I
a = −2.17771 + 1.34335I
b = 3.93843 + 1.30440I
9.7900 + 15.9619I 0
u = 0.091771 + 0.497640I
a = −1.02382 + 1.03092I
b = 0.236589 + 0.194531I
1.46452 + 1.15591I 2.35576 − 1.43742I
u = 0.091771 − 0.497640I
a = −1.02382 − 1.03092I
b = 0.236589 − 0.194531I
1.46452 − 1.15591I 2.35576 + 1.43742I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167885 + 0.261248I
a = −2.16440 − 0.06411I
b = −0.807671 + 0.534557I
−1.92776 + 0.81013I −4.46723 − 0.15914I
u = −0.167885 − 0.261248I
a = −2.16440 + 0.06411I
b = −0.807671 − 0.534557I
−1.92776 − 0.81013I −4.46723 + 0.15914I
12
II. I
u
2
= hb − u + 1, u
2
+ a − u, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
11
=
−u
2
+ u
u − 1
a
4
=
−u
2
− 1
−2u
2
+ 3u
a
8
=
−u
2
+ 1
u
2
a
1
=
u
2
− 1
−u
2
a
5
=
−u
−u
2
+ u + 1
a
9
=
0
−u
a
10
=
−u
2
+ u
u − 1
a
12
=
−u
2
+ u
2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
+ 8u − 16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
12
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
, c
4
u
3
+ 2u
2
+ u + 1
c
6
u
3
− u
2
+ 1
c
7
, c
8
u
3
+ u
2
+ 2u + 1
c
9
(u − 1)
3
c
10
u
3
c
11
(u + 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
8
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
6
y
3
− y
2
+ 2y −1
c
3
, c
4
y
3
− 2y
2
− 3y −1
c
9
, c
11
(y −1)
3
c
10
y
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.662359 − 0.562280I
b = −0.122561 + 0.744862I
1.37919 − 2.82812I −9.19557 + 4.65175I
u = 0.877439 − 0.744862I
a = 0.662359 + 0.562280I
b = −0.122561 − 0.744862I
1.37919 + 2.82812I −9.19557 − 4.65175I
u = −0.754878
a = −1.32472
b = −1.75488
−2.75839 −22.6090
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
− u
2
+ 2u − 1)(u
72
+ 14u
71
+ ··· + u + 1)
c
2
(u
3
+ u
2
− 1)(u
72
− 2u
71
+ ··· + 3u + 1)
c
3
(u
3
+ 2u
2
+ u + 1)(u
72
− 3u
71
+ ··· − 164u − 53)
c
4
(u
3
+ 2u
2
+ u + 1)(u
72
− 5u
71
+ ··· − 32u + 1)
c
6
(u
3
− u
2
+ 1)(u
72
− 2u
71
+ ··· + 3u + 1)
c
7
, c
8
(u
3
+ u
2
+ 2u + 1)(u
72
+ 14u
71
+ ··· + u + 1)
c
9
((u − 1)
3
)(u
72
− 4u
71
+ ··· + 2u − 1)
c
10
u
3
(u
72
+ 11u
71
+ ··· − 4u + 8)
c
11
((u + 1)
3
)(u
72
− 4u
71
+ ··· + 2u − 1)
c
12
(u
3
− u
2
+ 2u − 1)(u
72
+ 4u
71
+ ··· − u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
8
(y
3
+ 3y
2
+ 2y −1)(y
72
+ 90y
71
+ ··· + 123y + 1)
c
2
, c
6
(y
3
− y
2
+ 2y −1)(y
72
− 14y
71
+ ··· − y + 1)
c
3
(y
3
− 2y
2
− 3y −1)(y
72
− 79y
71
+ ··· + 38824y + 2809)
c
4
(y
3
− 2y
2
− 3y −1)(y
72
− 59y
71
+ ··· − 416y + 1)
c
9
, c
11
((y −1)
3
)(y
72
− 40y
71
+ ··· − 82y + 1)
c
10
y
3
(y
72
− 21y
71
+ ··· − 1872y + 64)
c
12
(y
3
+ 3y
2
+ 2y −1)(y
72
+ 14y
71
+ ··· − y + 1)
18
