12a
0654
(K12a
0654
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 8 2 6 11 5 1 9 4
Solving Sequence
2,7 3,10
4 1 11 6 8 5 9 12
c
2
c
3
c
1
c
10
c
6
c
7
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.44776 × 10
45
u
82
+ 1.88228 × 10
45
u
81
+ ··· + 4.67106 × 10
45
b − 4.92257 × 10
45
,
4.56361 × 10
45
u
82
+ 3.89164 × 10
45
u
81
+ ··· + 4.67106 × 10
45
a + 4.38504 × 10
45
, u
83
+ 2u
82
+ ··· + 2u − 1i
I
u
2
= h2b + 1, 2a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 84 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
= h1.45 × 10
45
u
82
+ 1.88 × 10
45
u
81
+ · · · + 4.67 × 10
45
b − 4.92 × 10
45
, 4.56 ×
10
45
u
82
+3.89×10
45
u
81
+· · ·+4.67×10
45
a+4.39×10
45
, u
83
+2u
82
+· · ·+2u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
−0.976996u
82
− 0.833138u
81
+ ··· − 1.67953u − 0.938767
−0.309942u
82
− 0.402967u
81
+ ··· − 0.857176u + 1.05384
a
4
=
0.490538u
82
+ 0.276265u
81
+ ··· + 1.57387u − 1.06664
0.136027u
82
+ 0.165051u
81
+ ··· + 0.892769u − 0.223335
a
1
=
−u
2
+ 1
−u
4
a
11
=
−1.04749u
82
− 0.897950u
81
+ ··· − 1.23217u − 1.87684
−1.54527u
82
− 1.66408u
81
+ ··· − 1.87786u + 1.38750
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
5
=
u
5
+ u
u
5
− u
3
+ u
a
9
=
−0.921584u
82
− 0.763915u
81
+ ··· + 0.687349u − 1.85196
−1.37611u
82
− 1.44172u
81
+ ··· − 0.552013u + 1.27476
a
12
=
0.374473u
82
+ 0.269946u
81
+ ··· + 3.53516u + 0.0915879
0.597808u
82
+ 0.580589u
81
+ ··· + 1.55233u − 0.354511
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.68031u
82
− 1.52488u
81
+ ··· − 2.18584u − 10.4378
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
83
+ 20u
82
+ ··· + 12u + 1
c
2
, c
6
u
83
− 2u
82
+ ··· + 2u + 1
c
3
u
83
+ u
82
+ ··· − 62u + 8
c
4
, c
12
u
83
+ 4u
82
+ ··· + 4u + 1
c
8
, c
11
u
83
− 2u
82
+ ··· − 35u + 4
c
9
2(2u
83
+ 13u
82
+ ··· − 65101u + 15173)
c
10
2(2u
83
+ 35u
82
+ ··· + 62u − 4)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
83
+ 88y
82
+ ··· − 40y −1
c
2
, c
6
y
83
− 20y
82
+ ··· + 12y −1
c
3
y
83
+ 9y
82
+ ··· − 2956y −64
c
4
, c
12
y
83
+ 60y
82
+ ··· + 12y −1
c
8
, c
11
y
83
− 52y
82
+ ··· + 1569y −16
c
9
4(4y
83
+ 507y
82
+ ··· + 8.37318 × 10
9
y −2.30220 × 10
8
)
c
10
4(4y
83
− 677y
82
+ ··· + 156y −16)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.903364 + 0.424677I
a = 1.53894 − 1.55609I
b = 0.888909 − 0.865193I
−1.93320 − 6.97812I 0
u = 0.903364 − 0.424677I
a = 1.53894 + 1.55609I
b = 0.888909 + 0.865193I
−1.93320 + 6.97812I 0
u = −0.867473 + 0.468864I
a = −1.15941 − 0.99435I
b = −0.875451 − 0.381159I
1.31046 + 3.33552I 0
u = −0.867473 − 0.468864I
a = −1.15941 + 0.99435I
b = −0.875451 + 0.381159I
1.31046 − 3.33552I 0
u = −1.042220 + 0.035267I
a = −0.793950 − 0.624964I
b = 0.087591 + 0.119886I
−8.94189 − 6.52162I 0
u = −1.042220 − 0.035267I
a = −0.793950 + 0.624964I
b = 0.087591 − 0.119886I
−8.94189 + 6.52162I 0
u = −0.878924 + 0.323578I
a = 0.58100 − 1.29209I
b = 1.053830 − 0.003673I
−6.40049 + 4.26517I −17.4265 − 8.0576I
u = −0.878924 − 0.323578I
a = 0.58100 + 1.29209I
b = 1.053830 + 0.003673I
−6.40049 − 4.26517I −17.4265 + 8.0576I
u = 0.813017 + 0.384092I
a = −0.00859 − 1.76199I
b = 0.676319 − 0.764949I
−2.07969 − 1.17143I −10.66001 + 4.16977I
u = 0.813017 − 0.384092I
a = −0.00859 + 1.76199I
b = 0.676319 + 0.764949I
−2.07969 + 1.17143I −10.66001 − 4.16977I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420879 + 0.791590I
a = −0.598628 − 0.823093I
b = 0.147354 − 0.727487I
−3.58940 − 5.15177I −8.49512 + 7.35556I
u = 0.420879 − 0.791590I
a = −0.598628 + 0.823093I
b = 0.147354 + 0.727487I
−3.58940 + 5.15177I −8.49512 − 7.35556I
u = 1.013160 + 0.441729I
a = −1.39941 + 1.30714I
b = −1.24596 + 0.86067I
−6.5398 − 12.7131I 0
u = 1.013160 − 0.441729I
a = −1.39941 − 1.30714I
b = −1.24596 − 0.86067I
−6.5398 + 12.7131I 0
u = 0.823581 + 0.346061I
a = 0.938555 − 0.307109I
b = 0.017949 + 0.810468I
−2.23914 − 2.76864I −10.20780 + 5.54130I
u = 0.823581 − 0.346061I
a = 0.938555 + 0.307109I
b = 0.017949 − 0.810468I
−2.23914 + 2.76864I −10.20780 − 5.54130I
u = −1.027830 + 0.414105I
a = 1.072000 + 0.556379I
b = 0.807846 + 0.347687I
−1.47818 + 7.11634I 0
u = −1.027830 − 0.414105I
a = 1.072000 − 0.556379I
b = 0.807846 − 0.347687I
−1.47818 − 7.11634I 0
u = 0.849599 + 0.221125I
a = −2.26382 + 0.89058I
b = −1.08261 + 1.27189I
−6.96103 − 0.26061I −19.4591 + 2.1398I
u = 0.849599 − 0.221125I
a = −2.26382 − 0.89058I
b = −1.08261 − 1.27189I
−6.96103 + 0.26061I −19.4591 − 2.1398I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.119060 + 0.149420I
a = 0.014858 − 0.335944I
b = −0.0823966 − 0.0099121I
−3.26358 + 0.42527I 0
u = 1.119060 − 0.149420I
a = 0.014858 + 0.335944I
b = −0.0823966 + 0.0099121I
−3.26358 − 0.42527I 0
u = 1.040690 + 0.521910I
a = 0.526785 + 0.646610I
b = 0.404797 + 0.655754I
−5.61244 + 0.29360I 0
u = 1.040690 − 0.521910I
a = 0.526785 − 0.646610I
b = 0.404797 − 0.655754I
−5.61244 − 0.29360I 0
u = −0.821548 + 0.039013I
a = 1.29461 + 1.50651I
b = −0.177155 + 0.529657I
−3.92182 − 2.53293I −15.8807 + 3.5355I
u = −0.821548 − 0.039013I
a = 1.29461 − 1.50651I
b = −0.177155 − 0.529657I
−3.92182 + 2.53293I −15.8807 − 3.5355I
u = −0.766501 + 0.262948I
a = 1.81596 + 2.07437I
b = 1.52642 + 0.91294I
−2.76379 + 0.97508I −6.89224 − 7.86392I
u = −0.766501 − 0.262948I
a = 1.81596 − 2.07437I
b = 1.52642 − 0.91294I
−2.76379 − 0.97508I −6.89224 + 7.86392I
u = −0.790665 + 0.889461I
a = −0.244409 − 0.580618I
b = −1.047370 − 0.292537I
4.25321 + 0.83445I 0
u = −0.790665 − 0.889461I
a = −0.244409 + 0.580618I
b = −1.047370 + 0.292537I
4.25321 − 0.83445I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.296784 + 0.751744I
a = −0.88271 + 1.11039I
b = −1.005420 + 0.061637I
−4.20156 + 8.41815I −8.07283 − 5.37219I
u = 0.296784 − 0.751744I
a = −0.88271 − 1.11039I
b = −1.005420 − 0.061637I
−4.20156 − 8.41815I −8.07283 + 5.37219I
u = 0.866584 + 0.838849I
a = −1.30726 − 2.03836I
b = 0.96612 − 2.73538I
0.67550 + 1.26886I 0
u = 0.866584 − 0.838849I
a = −1.30726 + 2.03836I
b = 0.96612 + 2.73538I
0.67550 − 1.26886I 0
u = −0.493053 + 0.620271I
a = −0.475062 − 0.907891I
b = −0.726019 − 0.454031I
2.51378 + 0.71207I 0.10130 − 2.82742I
u = −0.493053 − 0.620271I
a = −0.475062 + 0.907891I
b = −0.726019 + 0.454031I
2.51378 − 0.71207I 0.10130 + 2.82742I
u = −0.898784 + 0.810830I
a = −1.43432 − 2.91147I
b = −4.36479 − 0.47405I
−1.15186 + 3.03659I 0
u = −0.898784 − 0.810830I
a = −1.43432 + 2.91147I
b = −4.36479 + 0.47405I
−1.15186 − 3.03659I 0
u = −0.883489 + 0.847983I
a = −0.011561 − 1.025510I
b = −0.483243 − 0.384493I
4.93081 + 0.82823I 0
u = −0.883489 − 0.847983I
a = −0.011561 + 1.025510I
b = −0.483243 + 0.384493I
4.93081 − 0.82823I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827619 + 0.907540I
a = 0.582232 − 1.120590I
b = 2.28595 − 0.07765I
7.28825 + 5.19382I 0
u = 0.827619 − 0.907540I
a = 0.582232 + 1.120590I
b = 2.28595 + 0.07765I
7.28825 − 5.19382I 0
u = 0.905252 + 0.834445I
a = 0.56959 − 2.38412I
b = 3.65243 − 0.24771I
3.60788 − 3.10972I 0
u = 0.905252 − 0.834445I
a = 0.56959 + 2.38412I
b = 3.65243 + 0.24771I
3.60788 + 3.10972I 0
u = −0.222378 + 0.734119I
a = 0.232483 + 0.795201I
b = 0.494757 + 0.344126I
1.10470 − 3.00500I −2.57507 + 5.88232I
u = −0.222378 − 0.734119I
a = 0.232483 − 0.795201I
b = 0.494757 − 0.344126I
1.10470 + 3.00500I −2.57507 − 5.88232I
u = −0.863508 + 0.881824I
a = 1.50552 + 1.41822I
b = 3.28866 − 0.82542I
6.32523 − 3.87244I 0
u = −0.863508 − 0.881824I
a = 1.50552 − 1.41822I
b = 3.28866 + 0.82542I
6.32523 + 3.87244I 0
u = −0.835831 + 0.913585I
a = −1.01212 − 1.38557I
b = −3.02573 + 0.47246I
2.43889 − 10.57610I 0
u = −0.835831 − 0.913585I
a = −1.01212 + 1.38557I
b = −3.02573 − 0.47246I
2.43889 + 10.57610I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.908266 + 0.846421I
a = 1.38371 − 6.19520I
b = 9.62883 + 1.19468I
3.44640 − 3.14601I 0
u = 0.908266 − 0.846421I
a = 1.38371 + 6.19520I
b = 9.62883 − 1.19468I
3.44640 + 3.14601I 0
u = 0.935118 + 0.817982I
a = 2.22383 + 0.50064I
b = 1.64728 + 2.62555I
0.46358 − 7.44816I 0
u = 0.935118 − 0.817982I
a = 2.22383 − 0.50064I
b = 1.64728 − 2.62555I
0.46358 + 7.44816I 0
u = −0.649711 + 0.386534I
a = 2.43843 − 5.61901I
b = −2.45848 − 3.04171I
−3.47334 + 1.58146I −6.1784 + 18.4226I
u = −0.649711 − 0.386534I
a = 2.43843 + 5.61901I
b = −2.45848 + 3.04171I
−3.47334 − 1.58146I −6.1784 − 18.4226I
u = −0.928311 + 0.832518I
a = −0.390054 + 0.231412I
b = −0.745951 + 0.234709I
4.79099 + 5.42555I 0
u = −0.928311 − 0.832518I
a = −0.390054 − 0.231412I
b = −0.745951 − 0.234709I
4.79099 − 5.42555I 0
u = 0.875426 + 0.888713I
a = −0.73965 + 1.34238I
b = −2.64419 + 0.03636I
9.82410 − 0.21205I 0
u = 0.875426 − 0.888713I
a = −0.73965 − 1.34238I
b = −2.64419 − 0.03636I
9.82410 + 0.21205I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.921428 + 0.867054I
a = 0.233396 + 1.108810I
b = 1.72705 + 0.10982I
5.30400 + 3.21764I 0
u = −0.921428 − 0.867054I
a = 0.233396 − 1.108810I
b = 1.72705 − 0.10982I
5.30400 − 3.21764I 0
u = −0.959778 + 0.841390I
a = 0.44151 + 2.72265I
b = 3.23040 + 1.37772I
6.02022 + 10.25640I 0
u = −0.959778 − 0.841390I
a = 0.44151 − 2.72265I
b = 3.23040 − 1.37772I
6.02022 − 10.25640I 0
u = 0.956814 + 0.852374I
a = −0.73520 + 1.93512I
b = −2.65902 + 0.36412I
9.56432 − 6.22932I 0
u = 0.956814 − 0.852374I
a = −0.73520 − 1.93512I
b = −2.65902 − 0.36412I
9.56432 + 6.22932I 0
u = −1.009220 + 0.810934I
a = −0.492591 − 0.806285I
b = −1.105860 − 0.130163I
3.57288 + 5.47366I 0
u = −1.009220 − 0.810934I
a = −0.492591 + 0.806285I
b = −1.105860 + 0.130163I
3.57288 − 5.47366I 0
u = 0.993763 + 0.834217I
a = 0.77742 − 1.75218I
b = 2.38361 − 0.31041I
6.76065 − 11.62870I 0
u = 0.993763 − 0.834217I
a = 0.77742 + 1.75218I
b = 2.38361 + 0.31041I
6.76065 + 11.62870I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992985 + 0.841418I
a = −0.62638 − 2.41784I
b = −3.11949 − 0.89147I
1.9371 + 17.0537I 0
u = −0.992985 − 0.841418I
a = −0.62638 + 2.41784I
b = −3.11949 + 0.89147I
1.9371 − 17.0537I 0
u = −0.928501 + 0.915660I
a = 0.247842 + 0.800769I
b = 1.336460 + 0.203273I
5.15115 + 3.35326I 0
u = −0.928501 − 0.915660I
a = 0.247842 − 0.800769I
b = 1.336460 − 0.203273I
5.15115 − 3.35326I 0
u = 0.383689 + 0.567939I
a = 1.32258 − 0.75641I
b = 1.035080 − 0.296380I
−0.32611 + 3.23888I −4.94711 − 3.26188I
u = 0.383689 − 0.567939I
a = 1.32258 + 0.75641I
b = 1.035080 + 0.296380I
−0.32611 − 3.23888I −4.94711 + 3.26188I
u = 0.634371
a = −0.995682
b = 0.139931
−0.981408 −9.34690
u = 0.287381 + 0.485540I
a = 0.669167 + 0.138109I
b = 0.346077 + 0.799642I
−0.62428 − 1.90033I −3.73781 + 3.12702I
u = 0.287381 − 0.485540I
a = 0.669167 − 0.138109I
b = 0.346077 − 0.799642I
−0.62428 + 1.90033I −3.73781 − 3.12702I
u = 0.396872 + 0.223911I
a = −1.42774 + 0.52691I
b = 0.365573 − 0.125160I
−1.062230 + 0.044566I −7.83480 + 1.17242I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.396872 − 0.223911I
a = −1.42774 − 0.52691I
b = 0.365573 + 0.125160I
−1.062230 − 0.044566I −7.83480 − 1.17242I
u = −0.151974 + 0.394423I
a = −0.65974 + 3.24267I
b = −0.470123 + 0.500944I
−4.49038 − 1.51025I −9.82603 + 1.41859I
u = −0.151974 − 0.394423I
a = −0.65974 − 3.24267I
b = −0.470123 − 0.500944I
−4.49038 + 1.51025I −9.82603 − 1.41859I
13
II. I
u
2
= h2b + 1, 2a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
1
a
3
=
1
1
a
10
=
−0.5
−0.5
a
4
=
1
1
a
1
=
0
−1
a
11
=
−0.5
−1
a
6
=
1
1
a
8
=
−1
0
a
5
=
2
1
a
9
=
−1.5
−1
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9.75
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
12
u − 1
c
3
u
c
4
, c
6
, c
7
c
11
u + 1
c
9
, c
10
2(2u − 1)
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
11
, c
12
y −1
c
3
y
c
9
, c
10
4(4y −1)
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000
b = −0.500000
−3.28987 −9.75000
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)(u
83
+ 20u
82
+ ··· + 12u + 1)
c
2
(u − 1)(u
83
− 2u
82
+ ··· + 2u + 1)
c
3
u(u
83
+ u
82
+ ··· − 62u + 8)
c
4
(u + 1)(u
83
+ 4u
82
+ ··· + 4u + 1)
c
6
(u + 1)(u
83
− 2u
82
+ ··· + 2u + 1)
c
7
(u + 1)(u
83
+ 20u
82
+ ··· + 12u + 1)
c
8
(u − 1)(u
83
− 2u
82
+ ··· − 35u + 4)
c
9
4(2u − 1)(2u
83
+ 13u
82
+ ··· − 65101u + 15173)
c
10
4(2u − 1)(2u
83
+ 35u
82
+ ··· + 62u − 4)
c
11
(u + 1)(u
83
− 2u
82
+ ··· − 35u + 4)
c
12
(u − 1)(u
83
+ 4u
82
+ ··· + 4u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y −1)(y
83
+ 88y
82
+ ··· − 40y −1)
c
2
, c
6
(y −1)(y
83
− 20y
82
+ ··· + 12y −1)
c
3
y(y
83
+ 9y
82
+ ··· − 2956y −64)
c
4
, c
12
(y −1)(y
83
+ 60y
82
+ ··· + 12y −1)
c
8
, c
11
(y −1)(y
83
− 52y
82
+ ··· + 1569y −16)
c
9
16(4y −1)(4y
83
+ 507y
82
+ ··· + 8.37318 × 10
9
y −2.30220 × 10
8
)
c
10
16(4y −1)(4y
83
− 677y
82
+ ··· + 156y −16)
19
