12a
1028
(K12a
1028
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 11 2 3 12 1 6 5 9
Solving Sequence
2,6
7 3
8,11
5 12 10 4 1 9
c
6
c
2
c
7
c
5
c
11
c
10
c
4
c
1
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.85413 × 10
21
u
61
+ 5.58501 × 10
20
u
60
+ ··· + 1.19724 × 10
21
b + 4.72952 × 10
21
,
− 5.85942 × 10
20
u
61
− 1.64356 × 10
19
u
60
+ ··· + 1.79587 × 10
21
a − 5.76656 × 10
21
, u
62
− 2u
61
+ ··· − 3u + 3i
I
u
2
= h2b − a + u + 1, a
2
− 2au − 2a + u + 10, u
2
+ u − 1i
I
u
3
= hb, a + u − 1, u
2
− u − 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−1.85×10
21
u
61
+5.59×10
20
u
60
+· · ·+1.20×10
21
b+4.73×10
21
, −5.86×
10
20
u
61
−1.64×10
19
u
60
+· · ·+1.80×10
21
a−5.77×10
21
, u
62
−2u
61
+· · ·−3u+3i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
0.326273u
61
+ 0.00915189u
60
+ ··· + 0.583257u + 3.21102
1.54866u
61
− 0.466489u
60
+ ··· + 1.71535u − 3.95034
a
5
=
−1.89429u
61
+ 1.84617u
60
+ ··· − 2.84257u + 3.02775
0.503182u
61
− 0.156338u
60
+ ··· + 2.70916u − 0.866273
a
12
=
0.400730u
61
+ 0.0422853u
60
+ ··· + 6.28535u − 1.31710
−0.764399u
61
− 0.0338770u
60
+ ··· − 2.88357u + 2.08459
a
10
=
−1.22239u
61
+ 0.475640u
60
+ ··· − 1.13210u + 7.16135
1.54866u
61
− 0.466489u
60
+ ··· + 1.71535u − 3.95034
a
4
=
u
3
− 2u
u
5
− 3u
3
+ u
a
1
=
u
7
− 4u
5
+ 4u
3
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
9
=
−0.773448u
61
+ 0.634298u
60
+ ··· + 0.552568u + 6.07578
1.06704u
61
− 0.140676u
60
+ ··· + 1.68212u − 2.77517
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5453229852496626061797
598622430020480889203
u
61
+
4853186041595372948925
598622430020480889203
u
60
+ ··· +
14479600513782809331670
598622430020480889203
u +
12926322886540541438955
598622430020480889203
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
− 16u
61
+ ··· − 579u − 1233
c
2
, c
3
, c
6
c
7
u
62
− 2u
61
+ ··· − 3u + 3
c
4
u
62
− u
61
+ ··· + 1776u − 340
c
5
, c
10
, c
11
u
62
+ u
61
+ ··· + 28u
2
− 4
c
8
, c
9
, c
12
u
62
− 3u
61
+ ··· − 42u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
+ 28y
60
+ ··· − 15215085y + 1520289
c
2
, c
3
, c
6
c
7
y
62
− 72y
61
+ ··· − 165y + 9
c
4
y
62
− 3y
61
+ ··· − 1187616y + 115600
c
5
, c
10
, c
11
y
62
+ 57y
61
+ ··· − 224y + 16
c
8
, c
9
, c
12
y
62
− 57y
61
+ ··· + 1382y + 121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.007200 + 0.261088I
a = −0.41639 − 1.97038I
b = −0.267837 − 1.310190I
−1.60394 + 3.46351I 0
u = 1.007200 − 0.261088I
a = −0.41639 + 1.97038I
b = −0.267837 + 1.310190I
−1.60394 − 3.46351I 0
u = −1.07420
a = −0.365351
b = −0.698555
2.56229 0
u = −0.716351 + 0.566259I
a = 1.86955 − 1.69297I
b = −0.32576 − 1.41185I
0.79702 + 10.87260I 0. − 8.18899I
u = −0.716351 − 0.566259I
a = 1.86955 + 1.69297I
b = −0.32576 + 1.41185I
0.79702 − 10.87260I 0. + 8.18899I
u = 0.655993 + 0.571625I
a = 0.488575 + 1.010890I
b = −0.796895 + 0.259193I
6.11030 − 6.80886I 5.34073 + 7.16429I
u = 0.655993 − 0.571625I
a = 0.488575 − 1.010890I
b = −0.796895 − 0.259193I
6.11030 + 6.80886I 5.34073 − 7.16429I
u = −0.673724 + 0.494492I
a = −2.29323 + 1.43376I
b = 0.259258 + 1.374700I
−4.69108 + 6.74684I −3.12963 − 7.87910I
u = −0.673724 − 0.494492I
a = −2.29323 − 1.43376I
b = 0.259258 − 1.374700I
−4.69108 − 6.74684I −3.12963 + 7.87910I
u = 0.796177 + 0.213333I
a = 0.41466 + 2.30478I
b = 0.121032 + 1.385540I
−6.55517 + 0.85488I −7.88148 + 0.17264I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796177 − 0.213333I
a = 0.41466 − 2.30478I
b = 0.121032 − 1.385540I
−6.55517 − 0.85488I −7.88148 − 0.17264I
u = −0.564043 + 0.548667I
a = −0.447341 + 0.229699I
b = −0.443497 + 0.844170I
4.21718 + 2.38094I 3.74390 − 2.67056I
u = −0.564043 − 0.548667I
a = −0.447341 − 0.229699I
b = −0.443497 − 0.844170I
4.21718 − 2.38094I 3.74390 + 2.67056I
u = 0.594165 + 0.444538I
a = −0.836395 − 1.036370I
b = 0.639315 − 0.206105I
0.32482 − 3.45235I 2.17977 + 8.36980I
u = 0.594165 − 0.444538I
a = −0.836395 + 1.036370I
b = 0.639315 + 0.206105I
0.32482 + 3.45235I 2.17977 − 8.36980I
u = −0.571188 + 0.431106I
a = 2.56598 − 0.45376I
b = −0.178341 − 1.300370I
−2.75175 + 2.08926I −0.01721 − 4.13986I
u = −0.571188 − 0.431106I
a = 2.56598 + 0.45376I
b = −0.178341 + 1.300370I
−2.75175 − 2.08926I −0.01721 + 4.13986I
u = −0.387908 + 0.598457I
a = −1.019370 + 0.588574I
b = 0.373907 + 0.983797I
4.73467 + 1.53584I 5.00104 − 3.92364I
u = −0.387908 − 0.598457I
a = −1.019370 − 0.588574I
b = 0.373907 − 0.983797I
4.73467 − 1.53584I 5.00104 + 3.92364I
u = −1.28895
a = −0.201518
b = −0.778136
2.51819 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.204781 + 0.675940I
a = −0.420014 − 0.371051I
b = 0.324097 − 1.368980I
2.31037 − 6.69590I 3.77430 + 3.38945I
u = −0.204781 − 0.675940I
a = −0.420014 + 0.371051I
b = 0.324097 + 1.368980I
2.31037 + 6.69590I 3.77430 − 3.38945I
u = 0.281609 + 0.646493I
a = −0.595970 − 0.184571I
b = 0.786421 + 0.183473I
7.21336 + 2.69083I 8.17138 − 1.26728I
u = 0.281609 − 0.646493I
a = −0.595970 + 0.184571I
b = 0.786421 − 0.183473I
7.21336 − 2.69083I 8.17138 + 1.26728I
u = 0.523352 + 0.352342I
a = −1.00450 − 2.49502I
b = −0.04818 − 1.50583I
−3.44113 − 1.26231I 1.66254 + 5.76495I
u = 0.523352 − 0.352342I
a = −1.00450 + 2.49502I
b = −0.04818 + 1.50583I
−3.44113 + 1.26231I 1.66254 − 5.76495I
u = −0.582526 + 0.226332I
a = 0.359239 − 0.256336I
b = 0.236534 − 0.399039I
−1.067670 + 0.638295I −5.14268 − 1.93986I
u = −0.582526 − 0.226332I
a = 0.359239 + 0.256336I
b = 0.236534 + 0.399039I
−1.067670 − 0.638295I −5.14268 + 1.93986I
u = −0.202268 + 0.549474I
a = 0.632451 − 0.143815I
b = −0.214182 + 1.332140I
−3.33458 − 3.15272I 0.14004 + 2.65338I
u = −0.202268 − 0.549474I
a = 0.632451 + 0.143815I
b = −0.214182 − 1.332140I
−3.33458 + 3.15272I 0.14004 − 2.65338I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40914 + 0.13315I
a = 0.51047 + 1.56454I
b = −0.371460 + 1.155570I
−0.99301 − 4.15133I 0
u = 1.40914 − 0.13315I
a = 0.51047 − 1.56454I
b = −0.371460 − 1.155570I
−0.99301 + 4.15133I 0
u = −0.347757 + 0.431451I
a = 0.505172 + 0.967871I
b = 0.064547 − 1.219600I
−2.12115 + 0.99111I 2.00930 − 4.70377I
u = −0.347757 − 0.431451I
a = 0.505172 − 0.967871I
b = 0.064547 + 1.219600I
−2.12115 − 0.99111I 2.00930 + 4.70377I
u = 0.314628 + 0.395456I
a = 1.164540 + 0.306965I
b = −0.542566 − 0.070217I
1.123480 + 0.375315I 7.22919 − 0.47300I
u = 0.314628 − 0.395456I
a = 1.164540 − 0.306965I
b = −0.542566 + 0.070217I
1.123480 − 0.375315I 7.22919 + 0.47300I
u = 1.49488 + 0.02116I
a = −0.413812 − 0.671306I
b = 0.148317 − 1.100670I
−8.06794 − 2.22872I 0
u = 1.49488 − 0.02116I
a = −0.413812 + 0.671306I
b = 0.148317 + 1.100670I
−8.06794 + 2.22872I 0
u = −1.53366 + 0.06763I
a = −0.491620 + 0.585520I
b = 0.641533 + 0.140097I
−5.27774 + 0.82413I 0
u = −1.53366 − 0.06763I
a = −0.491620 − 0.585520I
b = 0.641533 − 0.140097I
−5.27774 − 0.82413I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55311 + 0.15223I
a = 0.506739 + 0.861351I
b = 0.548479 + 0.764285I
−2.85138 − 4.88620I 0
u = 1.55311 − 0.15223I
a = 0.506739 − 0.861351I
b = 0.548479 − 0.764285I
−2.85138 + 4.88620I 0
u = −1.56119 + 0.09638I
a = 0.23930 − 3.01008I
b = 0.09718 − 1.54436I
−10.56980 + 2.85407I 0
u = −1.56119 − 0.09638I
a = 0.23930 + 3.01008I
b = 0.09718 + 1.54436I
−10.56980 − 2.85407I 0
u = 1.56746 + 0.07050I
a = −0.298449 − 0.641796I
b = −0.346399 − 0.620690I
−8.41341 − 1.75030I 0
u = 1.56746 − 0.07050I
a = −0.298449 + 0.641796I
b = −0.346399 + 0.620690I
−8.41341 + 1.75030I 0
u = 1.56590 + 0.11660I
a = −1.66729 − 1.77178I
b = 0.247184 − 1.349610I
−9.98940 − 4.04036I 0
u = 1.56590 − 0.11660I
a = −1.66729 + 1.77178I
b = 0.247184 + 1.349610I
−9.98940 + 4.04036I 0
u = −1.57023 + 0.12495I
a = 0.179918 − 0.969880I
b = −0.707659 − 0.274637I
−6.99530 + 5.51319I 0
u = −1.57023 − 0.12495I
a = 0.179918 + 0.969880I
b = −0.707659 + 0.274637I
−6.99530 − 5.51319I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58497 + 0.17268I
a = 0.089269 + 1.024050I
b = 0.804752 + 0.322755I
−1.40796 + 9.56550I 0
u = −1.58497 − 0.17268I
a = 0.089269 − 1.024050I
b = 0.804752 − 0.322755I
−1.40796 − 9.56550I 0
u = 1.59444 + 0.14506I
a = 1.52867 + 2.29285I
b = −0.28220 + 1.40989I
−12.3648 − 9.1191I 0
u = 1.59444 − 0.14506I
a = 1.52867 − 2.29285I
b = −0.28220 − 1.40989I
−12.3648 + 9.1191I 0
u = 1.60987 + 0.17229I
a = −1.27643 − 2.49461I
b = 0.32114 − 1.44418I
−7.0545 − 13.6509I 0
u = 1.60987 − 0.17229I
a = −1.27643 + 2.49461I
b = 0.32114 + 1.44418I
−7.0545 + 13.6509I 0
u = −1.62128 + 0.05900I
a = −0.17888 + 2.84328I
b = −0.11167 + 1.44607I
−14.8365 + 0.1781I 0
u = −1.62128 − 0.05900I
a = −0.17888 − 2.84328I
b = −0.11167 − 1.44607I
−14.8365 − 0.1781I 0
u = 0.365613
a = 2.26862
b = −0.327163
1.07665 14.5070
u = 1.65789
a = 0.489935
b = 0.479321
−6.61187 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67622 + 0.04758I
a = 0.20931 − 2.66730I
b = 0.185218 − 1.328710I
−10.91160 − 2.40878I 0
u = −1.67622 − 0.04758I
a = 0.20931 + 2.66730I
b = 0.185218 + 1.328710I
−10.91160 + 2.40878I 0
11
II. I
u
2
= h2b − a + u + 1, a
2
− 2au − 2a + u + 10, u
2
+ u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u + 1
a
3
=
−u
−u + 1
a
8
=
u
u
a
11
=
a
1
2
a −
1
2
u −
1
2
a
5
=
1
2
au +
1
2
a −
1
2
u − 4
−2
a
12
=
−
1
2
a −
1
2
u −
1
2
−
1
2
a +
1
2
u +
1
2
a
10
=
1
2
a +
1
2
u +
1
2
1
2
a −
1
2
u −
1
2
a
4
=
−1
0
a
1
=
u
u
a
9
=
1
2
a +
3
2
u +
1
2
1
2
a +
1
2
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
(u
2
+ u − 1)
2
c
2
, c
3
(u
2
− u − 1)
2
c
4
, c
5
, c
10
c
11
(u
2
+ 2)
2
c
8
, c
9
(u − 1)
4
c
12
(u + 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
(y
2
− 3y + 1)
2
c
4
, c
5
, c
10
c
11
(y + 2)
4
c
8
, c
9
, c
12
(y −1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 1.61803 + 2.82843I
b = 1.414210I
−4.27683 −4.00000
u = 0.618034
a = 1.61803 − 2.82843I
b = − 1.414210I
−4.27683 −4.00000
u = −1.61803
a = −0.61803 + 2.82843I
b = 1.414210I
−12.1725 −4.00000
u = −1.61803
a = −0.61803 − 2.82843I
b = − 1.414210I
−12.1725 −4.00000
15
III. I
u
3
= hb, a + u − 1, u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u + 1
a
3
=
−u
−u − 1
a
8
=
−u
−u
a
11
=
−u + 1
0
a
5
=
1
0
a
12
=
−u + 1
0
a
10
=
−u + 1
0
a
4
=
1
0
a
1
=
u
u
a
9
=
−2u + 1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
u
2
+ u − 1
c
4
, c
5
, c
10
c
11
u
2
c
6
, c
7
u
2
− u − 1
c
8
, c
9
(u + 1)
2
c
12
(u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
y
2
− 3y + 1
c
4
, c
5
, c
10
c
11
y
2
c
8
, c
9
, c
12
(y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.61803
b = 0
0.657974 −6.00000
u = 1.61803
a = −0.618034
b = 0
−7.23771 −6.00000
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u − 1)
3
)(u
62
− 16u
61
+ ··· − 579u − 1233)
c
2
, c
3
((u
2
− u − 1)
2
)(u
2
+ u − 1)(u
62
− 2u
61
+ ··· − 3u + 3)
c
4
u
2
(u
2
+ 2)
2
(u
62
− u
61
+ ··· + 1776u − 340)
c
5
, c
10
, c
11
u
2
(u
2
+ 2)
2
(u
62
+ u
61
+ ··· + 28u
2
− 4)
c
6
, c
7
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
62
− 2u
61
+ ··· − 3u + 3)
c
8
, c
9
((u − 1)
4
)(u + 1)
2
(u
62
− 3u
61
+ ··· − 42u − 11)
c
12
((u − 1)
2
)(u + 1)
4
(u
62
− 3u
61
+ ··· − 42u − 11)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 3y + 1)
3
)(y
62
+ 28y
60
+ ··· − 1.52151 × 10
7
y + 1520289)
c
2
, c
3
, c
6
c
7
((y
2
− 3y + 1)
3
)(y
62
− 72y
61
+ ··· − 165y + 9)
c
4
y
2
(y + 2)
4
(y
62
− 3y
61
+ ··· − 1187616y + 115600)
c
5
, c
10
, c
11
y
2
(y + 2)
4
(y
62
+ 57y
61
+ ··· − 224y + 16)
c
8
, c
9
, c
12
((y −1)
6
)(y
62
− 57y
61
+ ··· + 1382y + 121)
21
