12a
0481
(K12a
0481
)
A knot diagram
1
Linearized knot diagam
3 6 11 10 7 2 12 1 5 4 9 8
Solving Sequence
7,12
8 1
2,9
6 3 5 10 4 11
c
7
c
12
c
8
c
6
c
2
c
5
c
9
c
4
c
11
c
1
, c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h8.33546 × 10
45
u
64
− 1.14445 × 10
46
u
63
+ ··· + 2.27514 × 10
46
b + 7.73936 × 10
46
,
− 6.97340 × 10
45
u
64
+ 1.87570 × 10
46
u
63
+ ··· + 6.82541 × 10
45
a − 1.64156 × 10
46
, u
65
− 3u
64
+ ··· − 8u − 3i
I
u
2
= ha
2
+ 2b − 2a + 1, a
4
− 4a
3
+ 4a
2
+ 3, u − 1i
I
u
3
= hb
2
− b + 1, a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 71 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
= h8.34×10
45
u
64
−1.14×10
46
u
63
+· · ·+2.28×10
46
b+7.74×10
46
, −6.97×
10
45
u
64
+1.88×10
46
u
63
+· · ·+6.83×10
45
a−1.64×10
46
, u
65
−3u
64
+· · ·−8u−3i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
2
=
1.02168u
64
− 2.74811u
63
+ ··· − 15.6860u + 2.40507
−0.366372u
64
+ 0.503023u
63
+ ··· − 12.2381u − 3.40171
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
1.66172u
64
− 2.35528u
63
+ ··· + 8.61379u − 3.26790
−0.319726u
64
+ 0.744780u
63
+ ··· + 1.79163u − 1.12739
a
3
=
2.25408u
64
− 3.92752u
63
+ ··· + 15.8897u + 9.78314
−1.38909u
64
+ 1.98660u
63
+ ··· − 19.4141u − 3.51898
a
5
=
1.34199u
64
− 1.61050u
63
+ ··· + 10.4054u − 4.39529
−0.319726u
64
+ 0.744780u
63
+ ··· + 1.79163u − 1.12739
a
10
=
1.60989u
64
− 4.21548u
63
+ ··· − 32.4505u − 3.49651
−0.276179u
64
+ 0.246100u
63
+ ··· − 7.07338u − 3.16209
a
4
=
1.03866u
64
− 1.95917u
63
+ ··· + 7.94157u + 7.99324
−0.995853u
64
+ 1.35764u
63
+ ··· − 16.0888u − 2.99309
a
11
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.575409u
64
− 1.03751u
63
+ ··· − 12.2400u + 0.321049
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
65
+ 22u
64
+ ··· − 29u − 9
c
2
, c
6
u
65
− 2u
64
+ ··· − u + 3
c
3
, c
4
, c
9
c
10
u
65
+ u
64
+ ··· − 16u − 4
c
7
, c
8
, c
12
u
65
− 3u
64
+ ··· − 8u − 3
c
11
u
65
+ 15u
64
+ ··· + 9984u + 2304
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
65
+ 46y
64
+ ··· − 2741y −81
c
2
, c
6
y
65
+ 22y
64
+ ··· − 29y −9
c
3
, c
4
, c
9
c
10
y
65
+ 75y
64
+ ··· − 192y −16
c
7
, c
8
, c
12
y
65
− 59y
64
+ ··· − 248y −9
c
11
y
65
− y
64
+ ··· − 97026048y −5308416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.888082 + 0.410833I
a = 0.646410 − 0.203115I
b = −0.654237 + 0.917487I
2.60919 − 2.94570I 5.59381 + 4.95414I
u = 0.888082 − 0.410833I
a = 0.646410 + 0.203115I
b = −0.654237 − 0.917487I
2.60919 + 2.94570I 5.59381 − 4.95414I
u = −0.303651 + 0.902592I
a = −1.11503 − 1.04244I
b = 0.723865 − 1.009450I
8.20289 − 9.66985I 4.28819 + 7.03671I
u = −0.303651 − 0.902592I
a = −1.11503 + 1.04244I
b = 0.723865 + 1.009450I
8.20289 + 9.66985I 4.28819 − 7.03671I
u = −0.357028 + 0.864794I
a = −0.120170 − 0.184351I
b = 0.810435 + 0.695902I
9.15604 − 3.90043I 6.04015 + 2.26901I
u = −0.357028 − 0.864794I
a = −0.120170 + 0.184351I
b = 0.810435 − 0.695902I
9.15604 + 3.90043I 6.04015 − 2.26901I
u = −0.871939 + 0.644664I
a = −1.166130 − 0.395613I
b = 0.775582 − 0.780086I
10.69910 − 1.33054I 0
u = −0.871939 − 0.644664I
a = −1.166130 + 0.395613I
b = 0.775582 + 0.780086I
10.69910 + 1.33054I 0
u = −1.071940 + 0.271690I
a = −1.51716 − 0.45745I
b = −0.059410 − 0.833219I
5.29432 + 0.38771I 0
u = −1.071940 − 0.271690I
a = −1.51716 + 0.45745I
b = −0.059410 + 0.833219I
5.29432 − 0.38771I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.956232 + 0.622330I
a = −0.508319 − 0.122319I
b = 0.730631 + 0.950916I
10.17330 + 4.36468I 0
u = −0.956232 − 0.622330I
a = −0.508319 + 0.122319I
b = 0.730631 − 0.950916I
10.17330 − 4.36468I 0
u = 0.746987 + 0.405773I
a = 1.373230 − 0.240037I
b = −0.663828 − 0.797440I
2.98112 + 2.17079I 7.43307 − 2.82107I
u = 0.746987 − 0.405773I
a = 1.373230 + 0.240037I
b = −0.663828 + 0.797440I
2.98112 − 2.17079I 7.43307 + 2.82107I
u = 0.262619 + 0.779561I
a = 1.28732 − 1.13527I
b = −0.685423 − 0.989058I
0.66485 + 7.27591I 1.08861 − 8.89845I
u = 0.262619 − 0.779561I
a = 1.28732 + 1.13527I
b = −0.685423 + 0.989058I
0.66485 − 7.27591I 1.08861 + 8.89845I
u = 1.20544
a = 1.04693
b = −0.442541
2.51098 0
u = −1.210530 + 0.121438I
a = −0.804093 + 0.106541I
b = 0.485668 + 1.012200I
2.34586 + 1.24708I 0
u = −1.210530 − 0.121438I
a = −0.804093 − 0.106541I
b = 0.485668 − 1.012200I
2.34586 − 1.24708I 0
u = 1.189940 + 0.262812I
a = 1.112030 − 0.471723I
b = −0.102185 − 0.962937I
−0.41777 + 1.70342I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.189940 − 0.262812I
a = 1.112030 + 0.471723I
b = −0.102185 + 0.962937I
−0.41777 − 1.70342I 0
u = 0.300846 + 0.705195I
a = 0.041328 − 0.304729I
b = −0.729277 + 0.685600I
1.57098 + 1.85327I 3.17798 − 4.14987I
u = 0.300846 − 0.705195I
a = 0.041328 + 0.304729I
b = −0.729277 − 0.685600I
1.57098 − 1.85327I 3.17798 + 4.14987I
u = −0.196519 + 0.709917I
a = −0.04566 + 1.82055I
b = −0.140059 + 1.043640I
2.74271 − 4.03109I −1.56032 + 4.30145I
u = −0.196519 − 0.709917I
a = −0.04566 − 1.82055I
b = −0.140059 − 1.043640I
2.74271 + 4.03109I −1.56032 − 4.30145I
u = 0.062464 + 0.696936I
a = 0.03481 + 1.70684I
b = 0.048122 + 1.014310I
−3.83534 + 1.80189I −6.00427 − 4.43623I
u = 0.062464 − 0.696936I
a = 0.03481 − 1.70684I
b = 0.048122 − 1.014310I
−3.83534 − 1.80189I −6.00427 + 4.43623I
u = −0.414473 + 0.549756I
a = −0.258906 + 0.215659I
b = −0.577074 + 0.179072I
6.60099 − 1.84186I 5.73903 + 3.43368I
u = −0.414473 − 0.549756I
a = −0.258906 − 0.215659I
b = −0.577074 − 0.179072I
6.60099 + 1.84186I 5.73903 − 3.43368I
u = −1.297190 + 0.268858I
a = −0.933747 − 0.495340I
b = 0.150814 − 1.077000I
0.40210 − 5.28798I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.297190 − 0.268858I
a = −0.933747 + 0.495340I
b = 0.150814 + 1.077000I
0.40210 + 5.28798I 0
u = −1.317890 + 0.155610I
a = −1.011440 − 0.057697I
b = 0.665716 − 0.212271I
4.57403 − 2.83927I 0
u = −1.317890 − 0.155610I
a = −1.011440 + 0.057697I
b = 0.665716 + 0.212271I
4.57403 + 2.83927I 0
u = −0.207623 + 0.592264I
a = −1.69337 − 1.29542I
b = 0.633445 − 0.958857I
−0.43277 − 3.63822I −2.67168 + 3.01987I
u = −0.207623 − 0.592264I
a = −1.69337 + 1.29542I
b = 0.633445 + 0.958857I
−0.43277 + 3.63822I −2.67168 − 3.01987I
u = 1.373270 + 0.150068I
a = 0.714513 + 0.181428I
b = −0.483932 + 1.111580I
9.70090 − 0.05073I 0
u = 1.373270 − 0.150068I
a = 0.714513 − 0.181428I
b = −0.483932 − 1.111580I
9.70090 + 0.05073I 0
u = −1.384540 + 0.118480I
a = 2.46352 − 0.66760I
b = −0.730700 + 0.918700I
9.31806 − 3.11523I 0
u = −1.384540 − 0.118480I
a = 2.46352 + 0.66760I
b = −0.730700 − 0.918700I
9.31806 + 3.11523I 0
u = 1.380960 + 0.184417I
a = −1.09435 + 1.47451I
b = 0.778406 − 0.728805I
5.42221 + 1.04361I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.380960 − 0.184417I
a = −1.09435 − 1.47451I
b = 0.778406 + 0.728805I
5.42221 − 1.04361I 0
u = 1.383180 + 0.238836I
a = −2.49505 − 0.01259I
b = 0.717910 + 0.982922I
4.64807 + 6.70673I 0
u = 1.383180 − 0.238836I
a = −2.49505 + 0.01259I
b = 0.717910 − 0.982922I
4.64807 − 6.70673I 0
u = −1.405930 + 0.052718I
a = 1.73085 + 1.30451I
b = −0.766620 − 0.820153I
9.62594 + 2.55262I 0
u = −1.405930 − 0.052718I
a = 1.73085 − 1.30451I
b = −0.766620 + 0.820153I
9.62594 − 2.55262I 0
u = 1.384210 + 0.280090I
a = 0.831833 − 0.504549I
b = −0.172242 − 1.152380I
7.78079 + 7.61615I 0
u = 1.384210 − 0.280090I
a = 0.831833 + 0.504549I
b = −0.172242 + 1.152380I
7.78079 − 7.61615I 0
u = −1.41598 + 0.27122I
a = 0.83745 + 1.23150I
b = −0.827312 − 0.681734I
7.04530 − 5.39041I 0
u = −1.41598 − 0.27122I
a = 0.83745 − 1.23150I
b = −0.827312 + 0.681734I
7.04530 + 5.39041I 0
u = 1.43155 + 0.20492I
a = 0.966638 − 0.073545I
b = −0.809524 − 0.220320I
12.46300 + 4.59312I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43155 − 0.20492I
a = 0.966638 + 0.073545I
b = −0.809524 + 0.220320I
12.46300 − 4.59312I 0
u = −1.41407 + 0.30946I
a = 2.26793 + 0.23939I
b = −0.726429 + 1.021480I
6.01152 − 11.21260I 0
u = −1.41407 − 0.30946I
a = 2.26793 − 0.23939I
b = −0.726429 − 1.021480I
6.01152 + 11.21260I 0
u = 1.45455 + 0.36028I
a = −2.06306 + 0.33688I
b = 0.740697 + 1.050510I
13.8214 + 14.2192I 0
u = 1.45455 − 0.36028I
a = −2.06306 − 0.33688I
b = 0.740697 − 1.050510I
13.8214 − 14.2192I 0
u = 1.46756 + 0.32998I
a = −0.765398 + 1.035260I
b = 0.879332 − 0.662994I
15.0130 + 8.2071I 0
u = 1.46756 − 0.32998I
a = −0.765398 − 1.035260I
b = 0.879332 + 0.662994I
15.0130 − 8.2071I 0
u = −0.237234 + 0.386656I
a = 0.214919 − 0.937698I
b = 0.587428 + 0.735506I
0.293265 + 1.243780I −2.51844 − 2.93595I
u = −0.237234 − 0.386656I
a = 0.214919 + 0.937698I
b = 0.587428 − 0.735506I
0.293265 − 1.243780I −2.51844 + 2.93595I
u = 1.56257 + 0.02370I
a = −1.62357 − 0.63557I
b = 0.843446 + 0.892821I
19.3856 + 3.1221I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56257 − 0.02370I
a = −1.62357 + 0.63557I
b = 0.843446 − 0.892821I
19.3856 − 3.1221I 0
u = 0.172559 + 0.341650I
a = 0.289287 + 0.247747I
b = 0.296575 + 0.310433I
0.059571 + 0.856042I 1.59029 − 7.87693I
u = 0.172559 − 0.341650I
a = 0.289287 − 0.247747I
b = 0.296575 − 0.310433I
0.059571 − 0.856042I 1.59029 + 7.87693I
u = −0.101292 + 0.291578I
a = 2.21326 − 3.83264I
b = −0.518548 − 0.944155I
4.81440 + 1.86541I −0.02684 − 2.78315I
u = −0.101292 − 0.291578I
a = 2.21326 + 3.83264I
b = −0.518548 + 0.944155I
4.81440 − 1.86541I −0.02684 + 2.78315I
11
II. I
u
2
= ha
2
+ 2b − 2a + 1, a
4
− 4a
3
+ 4a
2
+ 3, u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
8
=
1
−1
a
1
=
1
0
a
2
=
a
−
1
2
a
2
+ a −
1
2
a
9
=
0
−1
a
6
=
−
1
2
a
3
+ a
2
−
1
2
a + 1
1
2
a
2
− a −
1
2
a
3
=
1
2
a
3
−
3
2
a
2
+
3
2
a −
1
2
−
1
2
a
2
+ a +
1
2
a
5
=
−
1
2
a
3
+
3
2
a
2
−
3
2
a +
1
2
1
2
a
2
− a −
1
2
a
10
=
−2
a − 2
a
4
=
1
2
a
3
−
3
2
a
2
+
3
2
a −
1
2
1
2
a
3
− 2a
2
+
5
2
a
a
11
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2a
2
+ 4a + 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
− u + 1)
2
c
3
, c
4
, c
9
c
10
(u
2
+ 2)
2
c
6
(u
2
+ u + 1)
2
c
7
, c
8
(u − 1)
4
c
11
u
4
c
12
(u + 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
9
c
10
(y + 2)
4
c
7
, c
8
, c
12
(y −1)
4
c
11
y
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.224745 + 0.707107I
b = −0.500000 + 0.866025I
6.57974 − 2.02988I 6.00000 + 3.46410I
u = 1.00000
a = −0.224745 − 0.707107I
b = −0.500000 − 0.866025I
6.57974 + 2.02988I 6.00000 − 3.46410I
u = 1.00000
a = 2.22474 + 0.70711I
b = −0.500000 − 0.866025I
6.57974 + 2.02988I 6.00000 − 3.46410I
u = 1.00000
a = 2.22474 − 0.70711I
b = −0.500000 + 0.866025I
6.57974 − 2.02988I 6.00000 + 3.46410I
15
III. I
u
3
= hb
2
− b + 1, a + 1, u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
−1
a
8
=
1
−1
a
1
=
−1
0
a
2
=
−1
b
a
9
=
0
−1
a
6
=
−b + 1
b − 1
a
3
=
0
b − 1
a
5
=
0
b − 1
a
10
=
0
−1
a
4
=
0
b − 1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b + 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
4
, c
9
c
10
, c
11
u
2
c
7
, c
8
(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
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
9
c
10
, c
11
y
2
c
7
, c
8
, c
12
(y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 0. − 3.46410I
u = −1.00000
a = −1.00000
b = 0.500000 − 0.866025I
1.64493 − 2.02988I 0. + 3.46410I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
− u + 1)
3
)(u
65
+ 22u
64
+ ··· − 29u − 9)
c
2
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
65
− 2u
64
+ ··· − u + 3)
c
3
, c
4
, c
9
c
10
u
2
(u
2
+ 2)
2
(u
65
+ u
64
+ ··· − 16u − 4)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
65
− 2u
64
+ ··· − u + 3)
c
7
, c
8
((u − 1)
4
)(u + 1)
2
(u
65
− 3u
64
+ ··· − 8u − 3)
c
11
u
6
(u
65
+ 15u
64
+ ··· + 9984u + 2304)
c
12
((u − 1)
2
)(u + 1)
4
(u
65
− 3u
64
+ ··· − 8u − 3)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
65
+ 46y
64
+ ··· − 2741y −81)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
65
+ 22y
64
+ ··· − 29y −9)
c
3
, c
4
, c
9
c
10
y
2
(y + 2)
4
(y
65
+ 75y
64
+ ··· − 192y −16)
c
7
, c
8
, c
12
((y −1)
6
)(y
65
− 59y
64
+ ··· − 248y −9)
c
11
y
6
(y
65
− y
64
+ ··· − 9.70260 × 10
7
y −5308416)
21
