12a
0062
(K12a
0062
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 8 4 1 12 6 10 9
Solving Sequence
1,8 4,9
7 3 2 6 12 10 11 5
c
8
c
7
c
3
c
1
c
6
c
12
c
9
c
11
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.34077 × 10
20
u
67
− 5.64426 × 10
21
u
66
+ ··· + 2.17039 × 10
21
b − 1.25825 × 10
18
,
9.54970 × 10
20
u
67
− 1.50190 × 10
22
u
66
+ ··· + 2.17039 × 10
21
a − 1.96214 × 10
22
, u
68
− 14u
67
+ ··· − 10u + 1i
I
u
2
= hb, −u
3
+ u
2
+ a − 3u + 2, u
4
− u
3
+ 3u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 72 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
=
h4.34×10
20
u
67
−5.64×10
21
u
66
+· · ·+2.17×10
21
b−1.26×10
18
, 9.55×10
20
u
67
−
1.50 × 10
22
u
66
+ · · · + 2.17 × 10
21
a − 1.96 × 10
22
, u
68
− 14u
67
+ · · · − 10u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−0.440000u
67
+ 6.91995u
66
+ ··· − 51.0249u + 9.04053
−0.200000u
67
+ 2.60058u
66
+ ··· − 4.04580u + 0.000579734
a
9
=
1
u
2
a
7
=
−0.00405814u
67
− 0.343186u
66
+ ··· − 4.75480u − 1.28000
0.599983u
67
− 8.39976u
66
+ ··· + 5.88404u − 0.600000
a
3
=
−1.04000u
67
+ 14.7200u
66
+ ··· − 67.3194u + 10.4464
−0.200000u
67
+ 2.60638u
66
+ ··· − 5.50377u + 0.00637708
a
2
=
0.240000u
67
− 4.32004u
66
+ ··· + 46.9162u − 9.67830
0.400000u
67
− 5.19826u
66
+ ··· + 5.86261u + 0.00173920
a
6
=
−0.604041u
67
+ 8.05658u
66
+ ··· − 10.6388u − 0.680000
0.599983u
67
− 8.39976u
66
+ ··· + 5.88404u − 0.600000
a
12
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
5
=
−0.600000u
67
+ 7.80002u
66
+ ··· − 15.7984u + 0.115959
0.400000u
67
− 5.20406u
66
+ ··· + 1.32058u − 0.00405814
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3420526093780033582661
1085192982908851054063
u
67
+
48060996190185886286483
1085192982908851054063
u
66
+ ··· −
55112703006359386129501
1085192982908851054063
u +
338580210667561528866
1085192982908851054063
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 35u
67
+ ··· + 4u + 1
c
2
, c
4
u
68
− 5u
67
+ ··· − 4u + 1
c
3
, c
7
u
68
− u
67
+ ··· + 56u + 16
c
5
, c
10
u
68
− 2u
67
+ ··· − 2u + 1
c
6
u
68
− 27u
67
+ ··· − 3136u + 256
c
8
, c
9
, c
11
c
12
u
68
+ 14u
67
+ ··· + 10u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
+ y
67
+ ··· + 28y + 1
c
2
, c
4
y
68
− 35y
67
+ ··· − 4y + 1
c
3
, c
7
y
68
− 27y
67
+ ··· − 3136y + 256
c
5
, c
10
y
68
+ 14y
67
+ ··· + 10y + 1
c
6
y
68
+ 21y
67
+ ··· + 1159168y + 65536
c
8
, c
9
, c
11
c
12
y
68
+ 82y
67
+ ··· + 58y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.702330 + 0.719314I
a = 0.952126 + 0.378495I
b = 0.903771 + 0.568632I
−2.49105 + 1.44096I 0
u = 0.702330 − 0.719314I
a = 0.952126 − 0.378495I
b = 0.903771 − 0.568632I
−2.49105 − 1.44096I 0
u = 0.544234 + 0.823097I
a = −0.90860 − 1.80587I
b = 0.787095 − 0.580214I
−2.86875 − 3.13470I 0
u = 0.544234 − 0.823097I
a = −0.90860 + 1.80587I
b = 0.787095 + 0.580214I
−2.86875 + 3.13470I 0
u = 0.554678 + 0.885053I
a = 0.646033 + 0.891159I
b = 0.597107 + 0.903347I
−2.45632 − 5.69189I 0
u = 0.554678 − 0.885053I
a = 0.646033 − 0.891159I
b = 0.597107 − 0.903347I
−2.45632 + 5.69189I 0
u = 0.044041 + 0.938846I
a = −0.528628 + 0.575298I
b = 1.110590 + 0.020786I
4.84823 − 0.01751I 0
u = 0.044041 − 0.938846I
a = −0.528628 − 0.575298I
b = 1.110590 − 0.020786I
4.84823 + 0.01751I 0
u = 0.230283 + 1.041890I
a = 0.383940 + 0.200681I
b = −1.096910 + 0.163946I
4.52428 − 4.84320I 0
u = 0.230283 − 1.041890I
a = 0.383940 − 0.200681I
b = −1.096910 − 0.163946I
4.52428 + 4.84320I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.886908 + 0.130997I
a = 0.83919 − 1.48134I
b = 0.994696 − 0.657373I
−4.23343 − 6.61569I 0
u = 0.886908 − 0.130997I
a = 0.83919 + 1.48134I
b = 0.994696 + 0.657373I
−4.23343 + 6.61569I 0
u = 0.546801 + 0.959276I
a = 0.40211 + 1.46872I
b = −1.034870 + 0.568640I
1.73487 − 6.55266I 0
u = 0.546801 − 0.959276I
a = 0.40211 − 1.46872I
b = −1.034870 − 0.568640I
1.73487 + 6.55266I 0
u = 0.436383 + 0.725717I
a = −0.273836 − 0.549948I
b = −0.357436 − 0.624973I
−0.02388 − 1.90291I 0
u = 0.436383 − 0.725717I
a = −0.273836 + 0.549948I
b = −0.357436 + 0.624973I
−0.02388 + 1.90291I 0
u = 0.622290 + 0.972314I
a = −0.20600 − 1.69264I
b = 1.083880 − 0.702661I
−0.92862 − 11.62150I 0
u = 0.622290 − 0.972314I
a = −0.20600 + 1.69264I
b = 1.083880 + 0.702661I
−0.92862 + 11.62150I 0
u = 0.629333 + 0.462894I
a = −0.551587 + 0.229434I
b = −0.726711 − 0.032227I
−0.53973 − 2.02451I 0
u = 0.629333 − 0.462894I
a = −0.551587 − 0.229434I
b = −0.726711 + 0.032227I
−0.53973 + 2.02451I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.777439 + 0.035182I
a = 0.30993 + 1.86167I
b = 0.674208 + 0.749747I
−5.22617 − 1.25451I 0
u = 0.777439 − 0.035182I
a = 0.30993 − 1.86167I
b = 0.674208 − 0.749747I
−5.22617 + 1.25451I 0
u = 0.763667 + 0.147169I
a = −0.491078 + 1.269610I
b = −0.831426 + 0.522767I
−1.60097 − 2.14416I 0
u = 0.763667 − 0.147169I
a = −0.491078 − 1.269610I
b = −0.831426 − 0.522767I
−1.60097 + 2.14416I 0
u = 0.191467 + 0.685799I
a = 0.338418 − 0.572547I
b = 0.058134 − 0.732556I
0.37727 − 1.81277I 0
u = 0.191467 − 0.685799I
a = 0.338418 + 0.572547I
b = 0.058134 + 0.732556I
0.37727 + 1.81277I 0
u = −0.163052 + 0.684274I
a = −0.73814 + 2.00572I
b = 1.047110 + 0.475610I
2.97903 + 2.12216I 0
u = −0.163052 − 0.684274I
a = −0.73814 − 2.00572I
b = 1.047110 − 0.475610I
2.97903 − 2.12216I 0
u = −0.261785 + 0.643825I
a = 0.48024 − 2.41032I
b = −1.092870 − 0.650309I
0.60243 + 7.15138I 0
u = −0.261785 − 0.643825I
a = 0.48024 + 2.41032I
b = −1.092870 + 0.650309I
0.60243 − 7.15138I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.103387 + 0.574534I
a = −1.247280 + 0.459306I
b = −0.499622 + 0.853500I
−1.20136 + 1.57860I − 60.10 − 1.198988I
u = −0.103387 − 0.574534I
a = −1.247280 − 0.459306I
b = −0.499622 − 0.853500I
−1.20136 − 1.57860I − 60.10 + 1.198988I
u = 0.04488 + 1.47797I
a = −0.364667 + 0.130814I
b = −0.764119 + 0.387099I
5.14370 − 4.37032I 0
u = 0.04488 − 1.47797I
a = −0.364667 − 0.130814I
b = −0.764119 − 0.387099I
5.14370 + 4.37032I 0
u = 0.027008 + 0.463975I
a = 2.19954 − 2.38385I
b = −0.626899 − 0.429747I
−1.69854 − 0.64758I −0.10952 − 1.43549I
u = 0.027008 − 0.463975I
a = 2.19954 + 2.38385I
b = −0.626899 + 0.429747I
−1.69854 + 0.64758I −0.10952 + 1.43549I
u = −0.317474 + 0.289062I
a = −2.45267 + 0.04192I
b = −1.002640 + 0.554553I
−0.40550 − 4.98994I 1.72707 + 5.84738I
u = −0.317474 − 0.289062I
a = −2.45267 − 0.04192I
b = −1.002640 − 0.554553I
−0.40550 + 4.98994I 1.72707 − 5.84738I
u = 0.19316 + 1.55937I
a = 0.412184 + 0.175594I
b = 0.756526 + 0.443348I
4.94100 − 1.87633I 0
u = 0.19316 − 1.55937I
a = 0.412184 − 0.175594I
b = 0.756526 − 0.443348I
4.94100 + 1.87633I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00476 + 1.59773I
a = 1.24296 − 1.15996I
b = −0.933945 − 0.461744I
5.74571 − 0.74218I 0
u = 0.00476 − 1.59773I
a = 1.24296 + 1.15996I
b = −0.933945 + 0.461744I
5.74571 + 0.74218I 0
u = −0.01744 + 1.60580I
a = −0.375999 + 0.526599I
b = −0.542055 + 1.027890I
6.47914 + 1.94271I 0
u = −0.01744 − 1.60580I
a = −0.375999 − 0.526599I
b = −0.542055 − 1.027890I
6.47914 − 1.94271I 0
u = −0.06295 + 1.61402I
a = 0.65465 − 1.29562I
b = −1.162570 − 0.721984I
8.46752 + 8.29030I 0
u = −0.06295 − 1.61402I
a = 0.65465 + 1.29562I
b = −1.162570 + 0.721984I
8.46752 − 8.29030I 0
u = 0.03545 + 1.61491I
a = 0.181990 − 0.502218I
b = 0.261706 − 0.934865I
8.32968 − 2.56431I 0
u = 0.03545 − 1.61491I
a = 0.181990 + 0.502218I
b = 0.261706 + 0.934865I
8.32968 + 2.56431I 0
u = −0.03641 + 1.62694I
a = −0.761180 + 1.108760I
b = 1.165390 + 0.579784I
11.07740 + 2.81168I 0
u = −0.03641 − 1.62694I
a = −0.761180 − 1.108760I
b = 1.165390 − 0.579784I
11.07740 − 2.81168I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11902 + 1.64283I
a = −0.176746 − 0.516586I
b = −0.295103 − 0.928974I
8.22913 − 3.95284I 0
u = 0.11902 − 1.64283I
a = −0.176746 + 0.516586I
b = −0.295103 + 0.928974I
8.22913 + 3.95284I 0
u = 0.15043 + 1.64947I
a = −1.16212 − 1.17817I
b = 0.938536 − 0.488755I
5.56900 − 5.76525I 0
u = 0.15043 − 1.64947I
a = −1.16212 + 1.17817I
b = 0.938536 + 0.488755I
5.56900 + 5.76525I 0
u = 0.16104 + 1.66697I
a = 0.361534 + 0.570686I
b = 0.562537 + 1.028830I
6.26478 − 8.48321I 0
u = 0.16104 − 1.66697I
a = 0.361534 − 0.570686I
b = 0.562537 − 1.028830I
6.26478 + 8.48321I 0
u = 0.03764 + 1.68475I
a = −0.763999 + 0.214959I
b = 1.301930 + 0.098385I
14.11020 − 0.51006I 0
u = 0.03764 − 1.68475I
a = −0.763999 − 0.214959I
b = 1.301930 − 0.098385I
14.11020 + 0.51006I 0
u = 0.07476 + 1.69651I
a = 0.751083 + 0.197963I
b = −1.301690 + 0.120472I
14.0668 − 6.1535I 0
u = 0.07476 − 1.69651I
a = 0.751083 − 0.197963I
b = −1.301690 − 0.120472I
14.0668 + 6.1535I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16337 + 1.69140I
a = 0.702842 + 1.097820I
b = −1.159200 + 0.597520I
10.8412 − 9.4077I 0
u = 0.16337 − 1.69140I
a = 0.702842 − 1.097820I
b = −1.159200 − 0.597520I
10.8412 + 9.4077I 0
u = 0.18858 + 1.69551I
a = −0.584714 − 1.275720I
b = 1.156880 − 0.733784I
8.1698 − 14.8801I 0
u = 0.18858 − 1.69551I
a = −0.584714 + 1.275720I
b = 1.156880 + 0.733784I
8.1698 + 14.8801I 0
u = −0.239700 + 0.139703I
a = 2.88439 + 0.40526I
b = 0.899390 − 0.264675I
1.51732 − 0.60877I 6.10463 + 0.93946I
u = −0.239700 − 0.139703I
a = 2.88439 − 0.40526I
b = 0.899390 + 0.264675I
1.51732 + 0.60877I 6.10463 − 0.93946I
u = 0.072254 + 0.180965I
a = 3.84410 − 2.82042I
b = −0.371430 − 0.477509I
−1.77855 − 0.66427I −3.92098 − 1.34240I
u = 0.072254 − 0.180965I
a = 3.84410 + 2.82042I
b = −0.371430 + 0.477509I
−1.77855 + 0.66427I −3.92098 + 1.34240I
11
II. I
u
2
= hb, −u
3
+ u
2
+ a − 3u + 2, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
u
3
− u
2
+ 3u − 2
0
a
9
=
1
u
2
a
7
=
1
0
a
3
=
u
3
− u
2
+ 3u − 2
0
a
2
=
u
3
− u
2
+ 3u − 2
u
a
6
=
1
0
a
12
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
11
=
u
3
+ 2u
u
3
− u
2
+ 2u − 1
a
5
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
3
− 6u
2
+ 17u − 11
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
, c
7
u
4
c
4
(u + 1)
4
c
5
u
4
− u
3
+ u
2
+ 1
c
8
, c
9
u
4
− u
3
+ 3u
2
− 2u + 1
c
10
u
4
+ u
3
+ u
2
+ 1
c
11
, c
12
u
4
+ u
3
+ 3u
2
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
, c
7
y
4
c
5
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
8
, c
9
, c
11
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −0.95668 + 1.22719I
b = 0
−1.85594 − 1.41510I −5.13523 + 6.85627I
u = 0.395123 − 0.506844I
a = −0.95668 − 1.22719I
b = 0
−1.85594 + 1.41510I −5.13523 − 6.85627I
u = 0.10488 + 1.55249I
a = −0.043315 + 0.641200I
b = 0
5.14581 − 3.16396I 0.63523 + 2.29471I
u = 0.10488 − 1.55249I
a = −0.043315 − 0.641200I
b = 0
5.14581 + 3.16396I 0.63523 − 2.29471I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
68
+ 35u
67
+ ··· + 4u + 1)
c
2
((u − 1)
4
)(u
68
− 5u
67
+ ··· − 4u + 1)
c
3
, c
7
u
4
(u
68
− u
67
+ ··· + 56u + 16)
c
4
((u + 1)
4
)(u
68
− 5u
67
+ ··· − 4u + 1)
c
5
(u
4
− u
3
+ u
2
+ 1)(u
68
− 2u
67
+ ··· − 2u + 1)
c
6
u
4
(u
68
− 27u
67
+ ··· − 3136u + 256)
c
8
, c
9
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
68
+ 14u
67
+ ··· + 10u + 1)
c
10
(u
4
+ u
3
+ u
2
+ 1)(u
68
− 2u
67
+ ··· − 2u + 1)
c
11
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
68
+ 14u
67
+ ··· + 10u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
68
+ y
67
+ ··· + 28y + 1)
c
2
, c
4
((y −1)
4
)(y
68
− 35y
67
+ ··· − 4y + 1)
c
3
, c
7
y
4
(y
68
− 27y
67
+ ··· − 3136y + 256)
c
5
, c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
68
+ 14y
67
+ ··· + 10y + 1)
c
6
y
4
(y
68
+ 21y
67
+ ··· + 1159168y + 65536)
c
8
, c
9
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
68
+ 82y
67
+ ··· + 58y + 1)
17
