12n
0272
(K12n
0272
)
A knot diagram
1
Linearized knot diagam
3 4 10 2 9 4 12 3 6 8 7 11
Solving Sequence
3,10 4,6
7 2 1 9 5 8 11 12
c
3
c
6
c
2
c
1
c
9
c
5
c
8
c
10
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.07284 × 10
41
u
54
+ 1.52970 × 10
42
u
53
+ ··· + 1.46698 × 10
41
b − 3.05374 × 10
42
,
− 2.49859 × 10
42
u
54
− 5.62187 × 10
42
u
53
+ ··· + 3.66745 × 10
41
a + 2.92087 × 10
42
,
u
55
+ 2u
54
+ ··· + 16u − 5i
I
u
2
= hb
4
− 8b
3
u + 4b
3
− 2b
2
u − 18b
2
+ 28bu − 20b + 8u + 7, a + u − 1, u
2
− u + 1i
I
u
3
= hb
3
+ 6b
2
u + 3b
2
− 9b − 6u − 3, a − u − 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 69 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
= h6.07 × 10
41
u
54
+ 1.53 × 10
42
u
53
+ · · · + 1.47 × 10
41
b − 3.05 ×
10
42
, −2.50 × 10
42
u
54
− 5.62 × 10
42
u
53
+ · · · + 3.67 × 10
41
a + 2.92 ×
10
42
, u
55
+ 2u
54
+ · · · + 16u − 5i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
6.81288u
54
+ 15.3291u
53
+ ··· − 80.3573u − 7.96431
−4.13969u
54
− 10.4275u
53
+ ··· + 5.97193u + 20.8165
a
7
=
4.56016u
54
+ 9.52527u
53
+ ··· − 81.1963u + 4.33551
−3.61239u
54
− 8.85323u
53
+ ··· + 15.4827u + 14.3245
a
2
=
u
2
+ 1
u
4
a
1
=
u
4
+ u
2
+ 1
u
4
a
9
=
0.831512u
54
+ 0.329358u
53
+ ··· − 66.1006u + 20.4585
1.43416u
54
+ 0.946480u
53
+ ··· − 115.254u + 34.1944
a
5
=
u
4
+ u
2
+ 1
u
6
+ u
2
a
8
=
2.26567u
54
+ 1.27584u
53
+ ··· − 181.354u + 54.6529
1.43416u
54
+ 0.946480u
53
+ ··· − 115.254u + 34.1944
a
11
=
−0.582714u
54
− 5.23624u
53
+ ··· − 155.359u + 60.0525
−3.07932u
54
− 5.89630u
53
+ ··· + 75.6665u − 11.5791
a
12
=
3.31418u
54
+ 2.60263u
53
+ ··· − 230.938u + 66.8664
−4.10335u
54
− 10.8910u
53
+ ··· − 23.6437u + 30.3804
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.38419u
54
+ 9.98480u
53
+ ··· + 165.359u − 64.6148
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
55
+ 62u
54
+ ··· + 72966u − 625
c
2
, c
4
u
55
− 14u
54
+ ··· − 254u + 25
c
3
u
55
+ 2u
54
+ ··· + 16u − 5
c
5
, c
9
u
55
− 3u
54
+ ··· − 9u − 1
c
6
u
55
+ 6u
54
+ ··· + 856224u − 220279
c
7
, c
11
u
55
− u
54
+ ··· + 12u − 4
c
8
u
55
− 25u
53
+ ··· + 116957786u − 39721487
c
10
u
55
− 3u
54
+ ··· + 3164u − 748
c
12
u
55
− 25u
54
+ ··· + 80u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
55
− 130y
54
+ ··· + 3614843406y −390625
c
2
, c
4
y
55
+ 62y
54
+ ··· + 72966y −625
c
3
y
55
+ 14y
54
+ ··· − 254y −25
c
5
, c
9
y
55
− 15y
54
+ ··· + 43y −1
c
6
y
55
+ 46y
54
+ ··· − 1179952912654y −48522837841
c
7
, c
11
y
55
− 25y
54
+ ··· + 80y −16
c
8
y
55
− 50y
54
+ ··· + 12865645844702842y −1577796529491169
c
10
y
55
− 5y
54
+ ··· + 5379280y −559504
c
12
y
55
+ 15y
54
+ ··· − 2816y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643133 + 0.772247I
a = 0.073099 + 0.590591I
b = 0.874696 − 0.160448I
2.22767 − 6.23387I 3.64860 + 7.74824I
u = 0.643133 − 0.772247I
a = 0.073099 − 0.590591I
b = 0.874696 + 0.160448I
2.22767 + 6.23387I 3.64860 − 7.74824I
u = 0.541644 + 0.828095I
a = −0.038556 + 0.200004I
b = 0.699024 + 0.702967I
2.49097 + 1.59610I 3.71601 − 0.32055I
u = 0.541644 − 0.828095I
a = −0.038556 − 0.200004I
b = 0.699024 − 0.702967I
2.49097 − 1.59610I 3.71601 + 0.32055I
u = 0.255352 + 0.947684I
a = 0.566764 − 0.140113I
b = −0.528106 + 0.715239I
2.15852 + 1.39769I 6.44233 − 2.55277I
u = 0.255352 − 0.947684I
a = 0.566764 + 0.140113I
b = −0.528106 − 0.715239I
2.15852 − 1.39769I 6.44233 + 2.55277I
u = −0.733192 + 0.713911I
a = 0.798061 + 1.026100I
b = 0.52397 − 1.64587I
1.34086 + 4.85814I 3.75921 − 6.24399I
u = −0.733192 − 0.713911I
a = 0.798061 − 1.026100I
b = 0.52397 + 1.64587I
1.34086 − 4.85814I 3.75921 + 6.24399I
u = 0.245931 + 1.003490I
a = −0.180150 − 0.972673I
b = 0.19661 + 2.31761I
3.99628 − 2.15960I 12.20326 + 3.54467I
u = 0.245931 − 1.003490I
a = −0.180150 + 0.972673I
b = 0.19661 − 2.31761I
3.99628 + 2.15960I 12.20326 − 3.54467I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455933 + 0.952453I
a = −0.015920 + 0.377752I
b = 0.410151 − 1.298800I
0.26235 + 2.25660I 0. − 4.04903I
u = −0.455933 − 0.952453I
a = −0.015920 − 0.377752I
b = 0.410151 + 1.298800I
0.26235 − 2.25660I 0. + 4.04903I
u = −0.613118 + 0.670633I
a = 0.285325 − 0.526308I
b = 0.430171 − 0.004191I
−0.67943 + 1.91424I −0.34235 − 3.72747I
u = −0.613118 − 0.670633I
a = 0.285325 + 0.526308I
b = 0.430171 + 0.004191I
−0.67943 − 1.91424I −0.34235 + 3.72747I
u = −0.629710 + 0.956216I
a = 0.732740 + 0.781573I
b = 0.00414 − 2.05580I
2.14605 + 0.34842I 0
u = −0.629710 − 0.956216I
a = 0.732740 − 0.781573I
b = 0.00414 + 2.05580I
2.14605 − 0.34842I 0
u = −0.778599 + 0.329602I
a = 0.678856 − 0.803797I
b = 0.168770 − 0.052346I
−2.66054 + 0.76259I −1.67387 − 1.84877I
u = −0.778599 − 0.329602I
a = 0.678856 + 0.803797I
b = 0.168770 + 0.052346I
−2.66054 − 0.76259I −1.67387 + 1.84877I
u = 0.516920 + 1.032630I
a = 0.675627 − 0.596738I
b = −0.38124 + 1.87533I
2.33972 − 3.94259I 0
u = 0.516920 − 1.032630I
a = 0.675627 + 0.596738I
b = −0.38124 − 1.87533I
2.33972 + 3.94259I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.826976 + 0.174508I
a = 0.793904 + 0.895765I
b = 0.301796 + 0.056023I
−1.77909 + 4.14857I 0.53786 − 4.76792I
u = 0.826976 − 0.174508I
a = 0.793904 − 0.895765I
b = 0.301796 − 0.056023I
−1.77909 − 4.14857I 0.53786 + 4.76792I
u = −0.403926 + 1.086140I
a = −0.301206 + 0.696568I
b = 0.84782 − 1.88492I
−0.05616 + 3.61985I 0
u = −0.403926 − 1.086140I
a = −0.301206 − 0.696568I
b = 0.84782 + 1.88492I
−0.05616 − 3.61985I 0
u = 0.635290 + 0.539955I
a = 0.80977 − 1.17532I
b = 0.335753 + 1.218400I
0.699297 − 0.586817I 2.30186 − 0.73142I
u = 0.635290 − 0.539955I
a = 0.80977 + 1.17532I
b = 0.335753 − 1.218400I
0.699297 + 0.586817I 2.30186 + 0.73142I
u = 0.357804 + 1.146380I
a = −0.371516 − 0.795743I
b = 0.99860 + 2.21220I
1.55711 − 8.45299I 0
u = 0.357804 − 1.146380I
a = −0.371516 + 0.795743I
b = 0.99860 − 2.21220I
1.55711 + 8.45299I 0
u = −0.889584 + 0.849382I
a = −1.053920 + 0.046965I
b = 0.026656 + 0.258349I
−3.64967 − 0.17207I 0
u = −0.889584 − 0.849382I
a = −1.053920 − 0.046965I
b = 0.026656 − 0.258349I
−3.64967 + 0.17207I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.031113 + 0.765896I
a = −0.25903 + 1.40965I
b = −1.01707 − 2.10431I
5.48181 + 3.63285I 13.5953 − 4.3642I
u = −0.031113 − 0.765896I
a = −0.25903 − 1.40965I
b = −1.01707 + 2.10431I
5.48181 − 3.63285I 13.5953 + 4.3642I
u = −0.980350 + 0.786429I
a = −1.188620 + 0.046193I
b = −0.330725 + 0.677000I
−7.75967 − 8.08659I 0
u = −0.980350 − 0.786429I
a = −1.188620 − 0.046193I
b = −0.330725 − 0.677000I
−7.75967 + 8.08659I 0
u = 0.973285 + 0.826962I
a = −1.156140 − 0.078168I
b = −0.129976 − 0.669159I
−9.70239 + 2.43605I 0
u = 0.973285 − 0.826962I
a = −1.156140 + 0.078168I
b = −0.129976 + 0.669159I
−9.70239 − 2.43605I 0
u = −0.834739 + 0.982712I
a = 0.003646 − 1.048060I
b = −0.34032 + 2.13272I
−3.22528 + 6.57102I 0
u = −0.834739 − 0.982712I
a = 0.003646 + 1.048060I
b = −0.34032 − 2.13272I
−3.22528 − 6.57102I 0
u = −0.941255 + 0.925932I
a = 0.118357 − 1.083720I
b = −0.82877 + 1.42918I
−8.54383 − 0.44596I 0
u = −0.941255 − 0.925932I
a = 0.118357 + 1.083720I
b = −0.82877 − 1.42918I
−8.54383 + 0.44596I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.939126 + 0.931067I
a = −1.066090 − 0.168051I
b = 0.426943 − 0.559972I
−10.06640 − 1.58825I 0
u = 0.939126 − 0.931067I
a = −1.066090 + 0.168051I
b = 0.426943 + 0.559972I
−10.06640 + 1.58825I 0
u = −0.917840 + 0.968985I
a = −1.027200 + 0.203661I
b = 0.641384 + 0.467628I
−8.40289 + 7.27332I 0
u = −0.917840 − 0.968985I
a = −1.027200 − 0.203661I
b = 0.641384 − 0.467628I
−8.40289 − 7.27332I 0
u = 0.921796 + 0.966607I
a = 0.077249 + 1.095330I
b = −0.84619 − 1.72543I
−9.95240 − 5.24724I 0
u = 0.921796 − 0.966607I
a = 0.077249 − 1.095330I
b = −0.84619 + 1.72543I
−9.95240 + 5.24724I 0
u = 0.861727 + 1.038620I
a = −0.009790 + 1.107290I
b = −0.74617 − 2.39826I
−9.01329 − 9.17083I 0
u = 0.861727 − 1.038620I
a = −0.009790 − 1.107290I
b = −0.74617 + 2.39826I
−9.01329 + 9.17083I 0
u = −0.840461 + 1.058680I
a = −0.036507 − 1.110470I
b = −0.69938 + 2.61952I
−6.8786 + 14.7636I 0
u = −0.840461 − 1.058680I
a = −0.036507 + 1.110470I
b = −0.69938 − 2.61952I
−6.8786 − 14.7636I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.076743 + 0.576649I
a = −0.56089 + 1.77985I
b = −1.50038 − 1.35769I
4.70804 − 3.84497I 11.03034 + 2.81257I
u = 0.076743 − 0.576649I
a = −0.56089 − 1.77985I
b = −1.50038 + 1.35769I
4.70804 + 3.84497I 11.03034 − 2.81257I
u = 0.094139 + 0.557159I
a = −0.04524 − 1.86661I
b = −0.91864 + 1.34124I
2.17167 − 0.44148I 7.35335 + 0.00703I
u = 0.094139 − 0.557159I
a = −0.04524 + 1.86661I
b = −0.91864 − 1.34124I
2.17167 + 0.44148I 7.35335 − 0.00703I
u = 0.319907
a = 2.19474
b = −0.239033
1.23747 7.46610
10
II. I
u
2
= h−8b
3
u − 2b
2
u + · · · − 20b + 7, a + u − 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u − 1
a
6
=
−u + 1
b
a
7
=
b − 2u + 1
bu + 1
a
2
=
u
−u
a
1
=
0
−u
a
9
=
u − 1
−b + u
a
5
=
0
u
a
8
=
−b + 2u − 1
−b + u
a
11
=
−b
2
u + 2bu − 4b + 3u
−b
2
u + 2bu − 3b + 2u + 1
a
12
=
−2b
2
u + 4bu − 8b + 8u − 2
−b
3
u + b
3
− 5b
2
u − 2b
2
+ 9bu − 15b + 10u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
2
u − 4b
2
+ 8bu + 8b − 8u + 24
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
5
(u − 1)
8
c
6
u
8
− 4u
7
+ 8u
6
− 16u
5
+ 27u
4
− 24u
3
+ 24u
2
− 40u + 25
c
7
, c
11
(u
4
− 2u
2
+ 2)
2
c
8
u
8
+ 4u
7
+ 8u
6
+ 16u
5
+ 27u
4
+ 24u
3
+ 24u
2
+ 40u + 25
c
9
(u + 1)
8
c
10
(u
4
+ 2u
2
+ 2)
2
c
12
(u
2
− 2u + 2)
4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
(y
2
+ y + 1)
4
c
5
, c
9
(y − 1)
8
c
6
, c
8
y
8
− 10y
6
+ 32y
5
+ 75y
4
− 160y
3
+ 6y
2
− 400y + 625
c
7
, c
11
(y
2
− 2y + 2)
4
c
10
(y
2
+ 2y + 2)
4
c
12
(y
2
+ 4)
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = −0.723943 + 0.788589I
4.11234 + 1.63398I 10.00000 − 0.53590I
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = −1.17903 + 1.57683I
4.11234 − 5.69375I 10.00000 + 7.46410I
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 1.17903 + 1.88727I
4.11234 − 5.69375I 10.00000 + 7.46410I
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0.72394 + 2.67551I
4.11234 + 1.63398I 10.00000 − 0.53590I
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = −0.723943 − 0.788589I
4.11234 − 1.63398I 10.00000 + 0.53590I
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = −1.17903 − 1.57683I
4.11234 + 5.69375I 10.00000 − 7.46410I
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 1.17903 − 1.88727I
4.11234 + 5.69375I 10.00000 − 7.46410I
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0.72394 − 2.67551I
4.11234 − 1.63398I 10.00000 + 0.53590I
14
III. I
u
3
= hb
3
+ 6b
2
u + 3b
2
− 9b − 6u − 3, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u − 1
a
6
=
u + 1
b
a
7
=
b + 2u + 1
−bu + 1
a
2
=
−u
u
a
1
=
0
u
a
9
=
u + 1
b + u
a
5
=
0
−u
a
8
=
b + 2u + 1
b + u
a
11
=
−b
2
u + 2bu + 4b + 3u
−b
2
u + 2bu + 3b + 2u − 1
a
12
=
0
b
2
+ 4bu + 2b + u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2b
2
u − 2b
2
− 4bu + 4b + 2u + 10
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
(u
2
− u + 1)
3
c
2
, c
3
(u
2
+ u + 1)
3
c
5
(u + 1)
6
c
7
, c
10
, c
11
c
12
u
6
c
9
(u − 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
8
(y
2
+ y + 1)
3
c
5
, c
9
(y − 1)
6
c
7
, c
10
, c
11
c
12
y
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = − 1.73205I
1.64493 + 2.02988I 6.00000 − 3.46410I
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = − 1.73205I
1.64493 + 2.02988I 6.00000 − 3.46410I
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = − 1.73205I
1.64493 + 2.02988I 6.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 1.73205I
1.64493 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 1.73205I
1.64493 − 2.02988I 6.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 1.73205I
1.64493 − 2.02988I 6.00000 + 3.46410I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
7
)(u
55
+ 62u
54
+ ··· + 72966u − 625)
c
2
((u
2
+ u + 1)
7
)(u
55
− 14u
54
+ ··· − 254u + 25)
c
3
((u
2
− u + 1)
4
)(u
2
+ u + 1)
3
(u
55
+ 2u
54
+ ··· + 16u − 5)
c
4
((u
2
− u + 1)
7
)(u
55
− 14u
54
+ ··· − 254u + 25)
c
5
((u − 1)
8
)(u + 1)
6
(u
55
− 3u
54
+ ··· − 9u − 1)
c
6
((u
2
− u + 1)
3
)(u
8
− 4u
7
+ ··· − 40u + 25)
· (u
55
+ 6u
54
+ ··· + 856224u − 220279)
c
7
, c
11
u
6
(u
4
− 2u
2
+ 2)
2
(u
55
− u
54
+ ··· + 12u − 4)
c
8
((u
2
− u + 1)
3
)(u
8
+ 4u
7
+ ··· + 40u + 25)
· (u
55
− 25u
53
+ ··· + 116957786u − 39721487)
c
9
((u − 1)
6
)(u + 1)
8
(u
55
− 3u
54
+ ··· − 9u − 1)
c
10
u
6
(u
4
+ 2u
2
+ 2)
2
(u
55
− 3u
54
+ ··· + 3164u − 748)
c
12
u
6
(u
2
− 2u + 2)
4
(u
55
− 25u
54
+ ··· + 80u − 16)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
7
)(y
55
− 130y
54
+ ··· + 3.61484 × 10
9
y − 390625)
c
2
, c
4
((y
2
+ y + 1)
7
)(y
55
+ 62y
54
+ ··· + 72966y − 625)
c
3
((y
2
+ y + 1)
7
)(y
55
+ 14y
54
+ ··· − 254y − 25)
c
5
, c
9
((y − 1)
14
)(y
55
− 15y
54
+ ··· + 43y − 1)
c
6
((y
2
+ y + 1)
3
)(y
8
− 10y
6
+ ··· − 400y + 625)
· (y
55
+ 46y
54
+ ··· − 1179952912654y − 48522837841)
c
7
, c
11
y
6
(y
2
− 2y + 2)
4
(y
55
− 25y
54
+ ··· + 80y − 16)
c
8
((y
2
+ y + 1)
3
)(y
8
− 10y
6
+ ··· − 400y + 625)
· (y
55
− 50y
54
+ ··· + 12865645844702842y − 1577796529491169)
c
10
y
6
(y
2
+ 2y + 2)
4
(y
55
− 5y
54
+ ··· + 5379280y − 559504)
c
12
y
6
(y
2
+ 4)
4
(y
55
+ 15y
54
+ ··· − 2816y − 256)
20
