12a
0130
(K12a
0130
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 11 9 4 1 12 7 10
Solving Sequence
1,9 4,10
8 3 2 7 12 11 6 5
c
9
c
8
c
3
c
1
c
7
c
12
c
10
c
6
c
5
c
2
, c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.71551 × 10
48
u
81
− 3.44735 × 10
49
u
80
+ ··· + 8.87210 × 10
48
b + 2.83258 × 10
48
,
2.41231 × 10
48
u
81
− 5.91476 × 10
49
u
80
+ ··· + 1.77442 × 10
49
a − 5.95155 × 10
49
, u
82
− 21u
81
+ ··· − 6u + 1i
I
u
2
= hb, u
2
a + a
2
− au + 2u
2
+ 2a − u + 3, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 88 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
=
h1.72×10
48
u
81
−3.45×10
49
u
80
+· · ·+8.87×10
48
b+2.83×10
48
, 2.41×10
48
u
81
−
5.91 × 10
49
u
80
+ · · · + 1.77 × 10
49
a − 5.95 × 10
49
, u
82
− 21u
81
+ · · · − 6u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
−0.135949u
81
+ 3.33335u
80
+ ··· − 14.6043u + 3.35408
−0.193360u
81
+ 3.88560u
80
+ ··· − 1.25258u − 0.319268
a
10
=
1
u
2
a
8
=
0.279029u
81
− 5.76662u
80
+ ··· − 2.69338u − 0.263304
0.124157u
81
− 2.30644u
80
+ ··· + 0.756435u − 0.180204
a
3
=
0.423190u
81
− 8.54849u
80
+ ··· − 15.2890u + 3.49093
0.112206u
81
− 2.46762u
80
+ ··· − 4.37396u + 0.0898841
a
2
=
−1.77927u
81
+ 36.7421u
80
+ ··· − 25.6185u + 3.03635
−0.339356u
81
+ 7.17752u
80
+ ··· − 1.91577u + 0.353373
a
7
=
0.154872u
81
− 3.46018u
80
+ ··· − 3.44981u − 0.0831007
0.124157u
81
− 2.30644u
80
+ ··· + 0.756435u − 0.180204
a
12
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−0.180204u
81
+ 3.66012u
80
+ ··· − 5.94908u + 0.324786
−0.0929984u
81
+ 2.05540u
80
+ ··· − 1.41087u + 0.279029
a
5
=
0.347186u
81
− 7.10288u
80
+ ··· − 17.9030u + 3.60140
0.0229512u
81
− 0.648699u
80
+ ··· − 3.43429u − 0.230274
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.00126u
81
− 124.839u
80
+ ··· + 77.6881u − 11.3348
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
82
+ 28u
81
+ ··· + 17u + 1
c
2
, c
5
u
82
+ 4u
81
+ ··· + u + 1
c
3
, c
8
u
82
− u
81
+ ··· + 224u + 64
c
6
, c
11
u
82
+ 3u
81
+ ··· − 3u
2
+ 1
c
7
u
82
− 35u
81
+ ··· − 62464u + 4096
c
9
, c
10
, c
12
u
82
+ 21u
81
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
82
+ 56y
81
+ ··· − 247y + 1
c
2
, c
5
y
82
+ 28y
81
+ ··· + 17y + 1
c
3
, c
8
y
82
− 35y
81
+ ··· − 62464y + 4096
c
6
, c
11
y
82
− 21y
81
+ ··· − 6y + 1
c
7
y
82
+ 13y
81
+ ··· + 200278016y + 16777216
c
9
, c
10
, c
12
y
82
+ 83y
81
+ ··· + 34y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966335 + 0.246919I
a = −0.915807 − 0.552310I
b = −0.932256 − 0.420934I
−0.0961212 − 0.0220843I 0
u = 0.966335 − 0.246919I
a = −0.915807 + 0.552310I
b = −0.932256 + 0.420934I
−0.0961212 + 0.0220843I 0
u = 0.868429 + 0.444440I
a = 0.686912 + 0.981827I
b = 0.754394 + 0.707664I
−5.26651 − 0.17540I 0
u = 0.868429 − 0.444440I
a = 0.686912 − 0.981827I
b = 0.754394 − 0.707664I
−5.26651 + 0.17540I 0
u = 0.835016 + 0.604230I
a = −0.11512 − 1.66139I
b = 0.906919 − 0.662661I
−4.79650 − 5.41790I 0
u = 0.835016 − 0.604230I
a = −0.11512 + 1.66139I
b = 0.906919 + 0.662661I
−4.79650 + 5.41790I 0
u = 0.735295 + 0.603136I
a = 0.401497 + 1.324250I
b = 0.548094 + 0.869830I
−1.46626 − 5.79986I 0
u = 0.735295 − 0.603136I
a = 0.401497 − 1.324250I
b = 0.548094 − 0.869830I
−1.46626 + 5.79986I 0
u = 1.003680 + 0.315252I
a = 0.993929 + 0.707315I
b = 0.984089 + 0.537506I
−0.98184 + 5.34647I 0
u = 1.003680 − 0.315252I
a = 0.993929 − 0.707315I
b = 0.984089 − 0.537506I
−0.98184 − 5.34647I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.658324 + 0.598113I
a = 0.485356 + 1.246000I
b = −0.843150 + 0.470953I
−0.30459 − 3.53700I 0
u = 0.658324 − 0.598113I
a = 0.485356 − 1.246000I
b = −0.843150 − 0.470953I
−0.30459 + 3.53700I 0
u = −0.117177 + 0.876232I
a = −0.486743 − 0.492557I
b = −1.077990 + 0.309869I
4.85512 − 5.44738I 0
u = −0.117177 − 0.876232I
a = −0.486743 + 0.492557I
b = −1.077990 − 0.309869I
4.85512 + 5.44738I 0
u = 0.838027 + 0.747480I
a = −0.18699 + 1.40186I
b = −1.077520 + 0.593293I
1.35820 − 5.83610I 0
u = 0.838027 − 0.747480I
a = −0.18699 − 1.40186I
b = −1.077520 − 0.593293I
1.35820 + 5.83610I 0
u = 0.887691 + 0.734910I
a = 0.24737 − 1.52308I
b = 1.093880 − 0.659857I
0.24237 − 11.48170I 0
u = 0.887691 − 0.734910I
a = 0.24737 + 1.52308I
b = 1.093880 + 0.659857I
0.24237 + 11.48170I 0
u = 0.635956 + 0.545968I
a = −0.179327 − 1.211200I
b = −0.459141 − 0.788281I
−0.506279 − 0.677239I 0
u = 0.635956 − 0.545968I
a = −0.179327 + 1.211200I
b = −0.459141 + 0.788281I
−0.506279 + 0.677239I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715873 + 0.435930I
a = −0.80244 − 1.80351I
b = 0.675859 − 0.557026I
−1.97685 + 0.93597I 0
u = 0.715873 − 0.435930I
a = −0.80244 + 1.80351I
b = 0.675859 + 0.557026I
−1.97685 − 0.93597I 0
u = −0.146062 + 0.758722I
a = 0.421743 + 0.799543I
b = 1.107210 − 0.191890I
5.29425 + 0.12843I 0
u = −0.146062 − 0.758722I
a = 0.421743 − 0.799543I
b = 1.107210 + 0.191890I
5.29425 − 0.12843I 0
u = 0.440280 + 1.196460I
a = −0.432093 + 0.139176I
b = −0.922439 − 0.078807I
4.33216 − 5.00431I 0
u = 0.440280 − 1.196460I
a = −0.432093 − 0.139176I
b = −0.922439 + 0.078807I
4.33216 + 5.00431I 0
u = 0.023208 + 1.284920I
a = −0.383313 + 0.281914I
b = −0.563238 + 0.690993I
1.17539 − 1.44130I 0
u = 0.023208 − 1.284920I
a = −0.383313 − 0.281914I
b = −0.563238 − 0.690993I
1.17539 + 1.44130I 0
u = 0.438517 + 1.303740I
a = 0.520590 + 0.015462I
b = 0.902982 + 0.290713I
3.99679 + 0.22630I 0
u = 0.438517 − 1.303740I
a = 0.520590 − 0.015462I
b = 0.902982 − 0.290713I
3.99679 − 0.22630I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.586540 + 0.193354I
a = −0.084170 − 0.399139I
b = −0.342644 − 0.399247I
−1.308760 − 0.330994I 0
u = 0.586540 − 0.193354I
a = −0.084170 + 0.399139I
b = −0.342644 + 0.399247I
−1.308760 + 0.330994I 0
u = −0.056956 + 1.397260I
a = 0.93185 − 1.30759I
b = −1.040060 − 0.573472I
2.65572 + 3.44471I 0
u = −0.056956 − 1.397260I
a = 0.93185 + 1.30759I
b = −1.040060 + 0.573472I
2.65572 − 3.44471I 0
u = 0.172171 + 1.400860I
a = −0.008660 − 0.390304I
b = −0.043316 − 0.693600I
3.77917 − 2.96134I 0
u = 0.172171 − 1.400860I
a = −0.008660 + 0.390304I
b = −0.043316 + 0.693600I
3.77917 + 2.96134I 0
u = 0.04901 + 1.42040I
a = 1.38947 − 0.82694I
b = −0.953515 − 0.285513I
4.58909 − 3.68918I 0
u = 0.04901 − 1.42040I
a = 1.38947 + 0.82694I
b = −0.953515 + 0.285513I
4.58909 + 3.68918I 0
u = −0.02690 + 1.43465I
a = −0.410227 + 0.611814I
b = −0.456620 + 1.092150I
5.98206 + 3.30923I 0
u = −0.02690 − 1.43465I
a = −0.410227 − 0.611814I
b = −0.456620 − 1.092150I
5.98206 − 3.30923I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12979 + 1.43945I
a = 0.57070 − 1.35363I
b = −1.216760 − 0.697773I
8.43626 + 9.73494I 0
u = −0.12979 − 1.43945I
a = 0.57070 + 1.35363I
b = −1.216760 + 0.697773I
8.43626 − 9.73494I 0
u = 0.01079 + 1.45064I
a = 0.316445 − 0.626909I
b = 0.342032 − 1.084310I
6.69030 − 2.27941I 0
u = 0.01079 − 1.45064I
a = 0.316445 + 0.626909I
b = 0.342032 + 1.084310I
6.69030 + 2.27941I 0
u = −0.00942 + 1.45315I
a = −0.952194 + 0.918789I
b = 1.116400 + 0.390200I
7.12609 + 0.70813I 0
u = −0.00942 − 1.45315I
a = −0.952194 − 0.918789I
b = 1.116400 − 0.390200I
7.12609 − 0.70813I 0
u = −0.10934 + 1.45497I
a = −0.587644 + 1.249560I
b = 1.233530 + 0.633587I
9.57155 + 3.83374I 0
u = −0.10934 − 1.45497I
a = −0.587644 − 1.249560I
b = 1.233530 − 0.633587I
9.57155 − 3.83374I 0
u = 0.31412 + 1.45604I
a = 0.388311 + 0.407195I
b = 0.586739 + 0.740171I
0.74863 − 4.43752I 0
u = 0.31412 − 1.45604I
a = 0.388311 − 0.407195I
b = 0.586739 − 0.740171I
0.74863 + 4.43752I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.444777 + 0.241252I
a = −1.29181 − 2.55165I
b = −1.116200 − 0.565155I
2.90706 + 7.74412I 3.19240 − 6.08323I
u = −0.444777 − 0.241252I
a = −1.29181 + 2.55165I
b = −1.116200 + 0.565155I
2.90706 − 7.74412I 3.19240 + 6.08323I
u = −0.403547 + 0.284113I
a = 1.11899 + 2.48613I
b = 1.108970 + 0.473452I
3.82381 + 2.08409I 5.12534 − 0.96293I
u = −0.403547 − 0.284113I
a = 1.11899 − 2.48613I
b = 1.108970 − 0.473452I
3.82381 − 2.08409I 5.12534 + 0.96293I
u = 0.22823 + 1.50166I
a = −1.25764 − 0.90746I
b = 0.956045 − 0.354047I
4.34801 − 2.40982I 0
u = 0.22823 − 1.50166I
a = −1.25764 + 0.90746I
b = 0.956045 + 0.354047I
4.34801 + 2.40982I 0
u = 0.22821 + 1.54217I
a = −0.259834 − 0.677815I
b = −0.395064 − 1.080160I
6.40684 − 3.91879I 0
u = 0.22821 − 1.54217I
a = −0.259834 + 0.677815I
b = −0.395064 + 1.080160I
6.40684 + 3.91879I 0
u = 0.23827 + 1.55598I
a = 0.854337 + 0.910276I
b = −1.111540 + 0.439099I
6.80534 − 6.93103I 0
u = 0.23827 − 1.55598I
a = 0.854337 − 0.910276I
b = −1.111540 − 0.439099I
6.80534 + 6.93103I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25959 + 1.55619I
a = 0.346137 + 0.684211I
b = 0.502939 + 1.091370I
5.60875 − 9.51344I 0
u = 0.25959 − 1.55619I
a = 0.346137 − 0.684211I
b = 0.502939 − 1.091370I
5.60875 + 9.51344I 0
u = 0.29684 + 1.55310I
a = −0.78073 − 1.26132I
b = 1.047760 − 0.610616I
2.18928 − 9.60793I 0
u = 0.29684 − 1.55310I
a = −0.78073 + 1.26132I
b = 1.047760 + 0.610616I
2.18928 + 9.60793I 0
u = 0.06659 + 1.58893I
a = −0.517511 + 0.119760I
b = 1.393120 + 0.025476I
13.42750 − 0.18395I 0
u = 0.06659 − 1.58893I
a = −0.517511 − 0.119760I
b = 1.393120 − 0.025476I
13.42750 + 0.18395I 0
u = 0.316207 + 0.256940I
a = 2.75499 − 0.01098I
b = −0.603808 + 0.128465I
−0.71341 − 2.60028I 1.59907 + 9.28858I
u = 0.316207 − 0.256940I
a = 2.75499 + 0.01098I
b = −0.603808 − 0.128465I
−0.71341 + 2.60028I 1.59907 − 9.28858I
u = 0.09605 + 1.60007I
a = 0.509209 + 0.059139I
b = −1.392400 + 0.070113I
13.3912 − 6.2552I 0
u = 0.09605 − 1.60007I
a = 0.509209 − 0.059139I
b = −1.392400 − 0.070113I
13.3912 + 6.2552I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29645 + 1.61228I
a = 0.480060 + 1.172130I
b = −1.220590 + 0.664279I
9.06027 − 10.15210I 0
u = 0.29645 − 1.61228I
a = 0.480060 − 1.172130I
b = −1.220590 − 0.664279I
9.06027 + 10.15210I 0
u = 0.31671 + 1.61338I
a = −0.452534 − 1.266320I
b = 1.204560 − 0.723604I
7.8725 − 16.0422I 0
u = 0.31671 − 1.61338I
a = −0.452534 + 1.266320I
b = 1.204560 + 0.723604I
7.8725 + 16.0422I 0
u = −0.308601 + 0.101944I
a = −1.34635 − 3.22772I
b = −0.811719 − 0.580510I
−2.19827 + 2.31052I −2.41183 − 3.57340I
u = −0.308601 − 0.101944I
a = −1.34635 + 3.22772I
b = −0.811719 + 0.580510I
−2.19827 − 2.31052I −2.41183 + 3.57340I
u = −0.104373 + 0.295289I
a = −0.47896 + 2.73242I
b = 0.825317 + 0.181714I
1.35824 + 0.44076I 6.52747 − 0.76489I
u = −0.104373 − 0.295289I
a = −0.47896 − 2.73242I
b = 0.825317 − 0.181714I
1.35824 − 0.44076I 6.52747 + 0.76489I
u = −0.010297 + 0.291539I
a = 2.15155 − 1.29958I
b = 0.099129 − 0.761027I
0.95053 − 2.17721I 1.51932 + 4.74837I
u = −0.010297 − 0.291539I
a = 2.15155 + 1.29958I
b = 0.099129 + 0.761027I
0.95053 + 2.17721I 1.51932 − 4.74837I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.155166 + 0.198549I
a = −2.63934 + 2.32241I
b = −0.310013 + 0.766636I
0.58271 + 2.77775I 0.95085 − 1.97842I
u = −0.155166 − 0.198549I
a = −2.63934 − 2.32241I
b = −0.310013 − 0.766636I
0.58271 − 2.77775I 0.95085 + 1.97842I
13
II. I
u
2
= hb, u
2
a + a
2
− au + 2u
2
+ 2a − u + 3, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
a
0
a
10
=
1
u
2
a
8
=
1
0
a
3
=
a
0
a
2
=
u
2
+ a − u + 2
u
a
7
=
1
0
a
12
=
u
u
2
− u + 1
a
11
=
u
2
+ 1
u
2
− u + 1
a
6
=
0
−u
a
5
=
a
u
2
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3au − 2u
2
+ a + 3u − 7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
, c
7
, c
8
u
6
c
6
(u
3
+ u
2
− 1)
2
c
9
, c
10
(u
3
− u
2
+ 2u − 1)
2
c
11
(u
3
− u
2
+ 1)
2
c
12
(u
3
+ u
2
+ 2u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
7
, c
8
y
6
c
6
, c
11
(y
3
− y
2
+ 2y −1)
2
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.706350 + 0.266290I
b = 0
3.02413 − 4.85801I −2.23639 + 5.66123I
u = 0.215080 + 1.307140I
a = 0.583789 + 0.478572I
b = 0
3.02413 − 0.79824I −0.946254 + 0.677361I
u = 0.215080 − 1.307140I
a = −0.706350 − 0.266290I
b = 0
3.02413 + 4.85801I −2.23639 − 5.66123I
u = 0.215080 − 1.307140I
a = 0.583789 − 0.478572I
b = 0
3.02413 + 0.79824I −0.946254 − 0.677361I
u = 0.569840
a = −0.87744 + 1.51977I
b = 0
−1.11345 + 2.02988I −5.31735 − 1.07831I
u = 0.569840
a = −0.87744 − 1.51977I
b = 0
−1.11345 − 2.02988I −5.31735 + 1.07831I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
3
)(u
82
+ 28u
81
+ ··· + 17u + 1)
c
2
((u
2
+ u + 1)
3
)(u
82
+ 4u
81
+ ··· + u + 1)
c
3
, c
8
u
6
(u
82
− u
81
+ ··· + 224u + 64)
c
5
((u
2
− u + 1)
3
)(u
82
+ 4u
81
+ ··· + u + 1)
c
6
((u
3
+ u
2
− 1)
2
)(u
82
+ 3u
81
+ ··· − 3u
2
+ 1)
c
7
u
6
(u
82
− 35u
81
+ ··· − 62464u + 4096)
c
9
, c
10
((u
3
− u
2
+ 2u − 1)
2
)(u
82
+ 21u
81
+ ··· + 6u + 1)
c
11
((u
3
− u
2
+ 1)
2
)(u
82
+ 3u
81
+ ··· − 3u
2
+ 1)
c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
82
+ 21u
81
+ ··· + 6u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
82
+ 56y
81
+ ··· − 247y + 1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
82
+ 28y
81
+ ··· + 17y + 1)
c
3
, c
8
y
6
(y
82
− 35y
81
+ ··· − 62464y + 4096)
c
6
, c
11
((y
3
− y
2
+ 2y −1)
2
)(y
82
− 21y
81
+ ··· − 6y + 1)
c
7
y
6
(y
82
+ 13y
81
+ ··· + 2.00278 × 10
8
y + 1.67772 × 10
7
)
c
9
, c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
82
+ 83y
81
+ ··· + 34y + 1)
19
