12a
0970
(K12a
0970
)
A knot diagram
1
Linearized knot diagam
4 6 10 1 9 3 11 12 2 7 8 5
Solving Sequence
7,11
8 12
3,9
6 2 5 10 4 1
c
7
c
11
c
8
c
6
c
2
c
5
c
10
c
3
c
1
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.53471 × 10
56
u
58
+ 1.42360 × 10
57
u
57
+ ··· + 3.93692 × 10
56
b − 1.65023 × 10
57
,
2.21537 × 10
57
u
58
+ 1.28547 × 10
58
u
57
+ ··· + 1.77161 × 10
57
a − 5.99824 × 10
58
, u
59
+ 6u
58
+ ··· − 41u − 9i
I
u
2
= hb + 3a + 1, 3a
2
+ 3a + 1, u
2
− u − 1i
I
u
3
= hb + 1, a
2
− 4a + 6, u + 1i
I
u
4
= hb − 1, a + 2, u + 1i
* 4 irreducible components of dim
C
= 0, with total 66 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
=
h3.53×10
56
u
58
+1.42×10
57
u
57
+· · ·+3.94×10
56
b−1.65×10
57
, 2.22×10
57
u
58
+
1.29 × 10
58
u
57
+ · · · + 1.77 × 10
57
a − 6.00 × 10
58
, u
59
+ 6u
58
+ · · · − 41u − 9i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
−1.25048u
58
− 7.25590u
57
+ ··· + 63.0832u + 33.8575
−0.897836u
58
− 3.61603u
57
+ ··· + 16.4208u + 4.19168
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
4.46863u
58
+ 17.9681u
57
+ ··· − 67.6860u + 1.25189
−5.38311u
58
− 23.1424u
57
+ ··· + 108.980u + 28.8269
a
2
=
2.90235u
58
+ 13.2229u
57
+ ··· − 72.6610u − 21.8095
−2.15803u
58
− 9.57659u
57
+ ··· + 48.5315u + 11.5997
a
5
=
−1.96408u
58
− 9.62149u
57
+ ··· + 68.3445u + 30.6108
3.54462u
58
+ 15.7106u
57
+ ··· − 88.3461u − 20.9626
a
10
=
−u
u
a
4
=
1.66279u
58
+ 5.41036u
57
+ ··· − 0.319179u + 15.6956
−3.81111u
58
− 16.2823u
57
+ ··· + 79.8231u + 22.3535
a
1
=
−3.00291u
58
− 15.3623u
57
+ ··· + 118.037u + 39.4455
1.06867u
58
+ 3.16422u
57
+ ··· + 9.35768u + 12.0523
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.777443u
58
+ 1.97110u
57
+ ··· − 73.4254u − 32.6128
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
59
− 3u
58
+ ··· + 8u
2
+ 2
c
2
, c
6
u
59
− 4u
58
+ ··· − 19u + 3
c
3
9(9u
59
+ 48u
58
+ ··· − 422003u + 85781)
c
5
9(9u
59
− 75u
58
+ ··· − 1270890u − 386003)
c
7
, c
8
, c
10
c
11
u
59
− 6u
58
+ ··· − 41u + 9
c
9
u
59
− 2u
58
+ ··· − 1152u + 432
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
59
+ 63y
58
+ ··· − 32y −4
c
2
, c
6
y
59
− 44y
58
+ ··· + 355y −9
c
3
81(81y
59
+ 1944y
58
+ ··· + 1.62773 × 10
10
y −7.35838 × 10
9
)
c
5
81(81y
59
− 5643y
58
+ ··· + 5.63820 × 10
12
y −1.48998 × 10
11
)
c
7
, c
8
, c
10
c
11
y
59
− 76y
58
+ ··· + 1483y −81
c
9
y
59
+ 22y
58
+ ··· − 1627776y −186624
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.857889 + 0.543473I
a = −0.935537 − 1.008220I
b = 1.210920 + 0.035673I
4.74114 − 0.35952I 0
u = −0.857889 − 0.543473I
a = −0.935537 + 1.008220I
b = 1.210920 − 0.035673I
4.74114 + 0.35952I 0
u = −0.130615 + 0.967990I
a = 0.190514 + 0.374185I
b = −1.318690 + 0.257478I
9.56415 − 6.01109I 0
u = −0.130615 − 0.967990I
a = 0.190514 − 0.374185I
b = −1.318690 − 0.257478I
9.56415 + 6.01109I 0
u = 0.948364 + 0.213838I
a = 1.51212 − 0.71166I
b = −1.37230 − 0.44609I
5.43776 + 2.93026I 0
u = 0.948364 − 0.213838I
a = 1.51212 + 0.71166I
b = −1.37230 + 0.44609I
5.43776 − 2.93026I 0
u = 0.960664 + 0.374018I
a = −0.305542 + 0.131521I
b = 0.126556 + 0.984052I
8.38003 + 6.19609I 0
u = 0.960664 − 0.374018I
a = −0.305542 − 0.131521I
b = 0.126556 − 0.984052I
8.38003 − 6.19609I 0
u = 0.969759 + 0.438458I
a = −1.42805 + 0.92716I
b = 1.37512 + 0.41779I
5.94572 + 7.83644I 0
u = 0.969759 − 0.438458I
a = −1.42805 − 0.92716I
b = 1.37512 − 0.41779I
5.94572 − 7.83644I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.066870 + 0.057775I
a = −1.208650 − 0.520306I
b = 1.291030 − 0.498774I
11.99040 + 0.77771I 0
u = 1.066870 − 0.057775I
a = −1.208650 + 0.520306I
b = 1.291030 + 0.498774I
11.99040 − 0.77771I 0
u = −0.764641 + 0.343047I
a = 1.330310 − 0.471171I
b = 0.362348 + 0.017749I
6.96622 − 0.49717I 6.23462 + 1.41414I
u = −0.764641 − 0.343047I
a = 1.330310 + 0.471171I
b = 0.362348 − 0.017749I
6.96622 + 0.49717I 6.23462 − 1.41414I
u = 0.799754 + 0.143772I
a = 0.272317 + 0.190800I
b = −0.120952 − 1.081830I
1.12793 + 2.71854I 10.64746 − 8.72932I
u = 0.799754 − 0.143772I
a = 0.272317 − 0.190800I
b = −0.120952 + 1.081830I
1.12793 − 2.71854I 10.64746 + 8.72932I
u = 1.046220 + 0.597660I
a = 1.28813 − 0.95719I
b = −1.38493 − 0.42023I
13.1773 + 11.1774I 0
u = 1.046220 − 0.597660I
a = 1.28813 + 0.95719I
b = −1.38493 + 0.42023I
13.1773 − 11.1774I 0
u = −1.21103
a = −1.33100
b = 0.716569
2.64173 0
u = −0.732538
a = 4.79896
b = −1.05042
2.92652 −31.4710
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.118101 + 0.722024I
a = 0.086917 − 0.358660I
b = 1.229760 − 0.250070I
2.59101 − 3.95881I 6.03862 + 7.13057I
u = −0.118101 − 0.722024I
a = 0.086917 + 0.358660I
b = 1.229760 + 0.250070I
2.59101 + 3.95881I 6.03862 − 7.13057I
u = −0.986283 + 0.810419I
a = 0.787138 + 0.653314I
b = −1.331550 − 0.064088I
11.99500 + 0.09773I 0
u = −0.986283 − 0.810419I
a = 0.787138 − 0.653314I
b = −1.331550 + 0.064088I
11.99500 − 0.09773I 0
u = −0.622166 + 0.142096I
a = −0.610096 + 0.520870I
b = −0.136025 + 0.091898I
1.150150 − 0.364893I 8.81978 + 0.27517I
u = −0.622166 − 0.142096I
a = −0.610096 − 0.520870I
b = −0.136025 − 0.091898I
1.150150 + 0.364893I 8.81978 − 0.27517I
u = −0.117244 + 0.612352I
a = 0.812578 − 0.945370I
b = 0.134811 − 0.595483I
5.05432 − 2.85507I 3.39383 + 3.61710I
u = −0.117244 − 0.612352I
a = 0.812578 + 0.945370I
b = 0.134811 + 0.595483I
5.05432 + 2.85507I 3.39383 − 3.61710I
u = −1.400890 + 0.081228I
a = 1.207210 + 0.357135I
b = −0.851572 − 0.540881I
6.44938 + 2.04861I 0
u = −1.400890 − 0.081228I
a = 1.207210 − 0.357135I
b = −0.851572 + 0.540881I
6.44938 − 2.04861I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420938 + 0.095647I
a = 3.99493 + 4.99920I
b = 0.990001 + 0.115515I
7.27721 − 0.14920I 10.48371 − 3.97631I
u = −0.420938 − 0.095647I
a = 3.99493 − 4.99920I
b = 0.990001 − 0.115515I
7.27721 + 0.14920I 10.48371 + 3.97631I
u = 0.392846 + 0.073015I
a = 1.305270 + 0.430518I
b = −0.582701 − 0.749020I
0.63593 + 2.21296I −5.75964 − 6.65166I
u = 0.392846 − 0.073015I
a = 1.305270 − 0.430518I
b = −0.582701 + 0.749020I
0.63593 − 2.21296I −5.75964 + 6.65166I
u = −0.195055 + 0.340133I
a = −1.55948 + 0.68613I
b = −1.091800 + 0.185883I
1.98756 − 0.99917I 2.40222 − 1.62487I
u = −0.195055 − 0.340133I
a = −1.55948 − 0.68613I
b = −1.091800 − 0.185883I
1.98756 + 0.99917I 2.40222 + 1.62487I
u = 1.61129 + 0.03030I
a = −0.088005 − 0.279498I
b = −0.217256 − 0.380886I
8.95456 + 0.95974I 0
u = 1.61129 − 0.03030I
a = −0.088005 + 0.279498I
b = −0.217256 + 0.380886I
8.95456 − 0.95974I 0
u = 0.068702 + 0.357326I
a = −1.24232 + 0.82388I
b = 0.092635 + 0.542344I
−0.908481 − 0.907750I −3.97873 + 3.36038I
u = 0.068702 − 0.357326I
a = −1.24232 − 0.82388I
b = 0.092635 − 0.542344I
−0.908481 + 0.907750I −3.97873 − 3.36038I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.66142
a = 2.81188
b = −1.21634
11.4761 0
u = 1.67528 + 0.06502I
a = 0.057515 + 0.457143I
b = 0.454603 + 0.532651I
15.6369 + 1.8583I 0
u = 1.67528 − 0.06502I
a = 0.057515 − 0.457143I
b = 0.454603 − 0.532651I
15.6369 − 1.8583I 0
u = −1.67823 + 0.03059I
a = 0.178129 − 0.749329I
b = −0.101652 + 1.402470I
9.97496 − 3.33073I 0
u = −1.67823 − 0.03059I
a = 0.178129 + 0.749329I
b = −0.101652 − 1.402470I
9.97496 + 3.33073I 0
u = 1.69183 + 0.11419I
a = −1.87237 + 0.56142I
b = 1.315370 + 0.125779I
13.68640 + 2.79097I 0
u = 1.69183 − 0.11419I
a = −1.87237 − 0.56142I
b = 1.315370 − 0.125779I
13.68640 − 2.79097I 0
u = −1.70433 + 0.05549I
a = 1.94975 + 0.14139I
b = −1.56251 + 0.59298I
14.8568 − 3.9980I 0
u = −1.70433 − 0.05549I
a = 1.94975 − 0.14139I
b = −1.56251 − 0.59298I
14.8568 + 3.9980I 0
u = −1.70709 + 0.09794I
a = −0.304137 + 0.494271I
b = 0.119151 − 1.247520I
17.7739 − 8.0669I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70709 − 0.09794I
a = −0.304137 − 0.494271I
b = 0.119151 + 1.247520I
17.7739 + 8.0669I 0
u = −1.70726 + 0.11689I
a = −1.95829 − 0.38629I
b = 1.51361 − 0.53501I
15.3175 − 10.0440I 0
u = −1.70726 − 0.11689I
a = −1.95829 + 0.38629I
b = 1.51361 + 0.53501I
15.3175 + 10.0440I 0
u = −1.73066 + 0.01255I
a = −1.72454 − 0.03435I
b = 1.50767 + 0.66940I
−17.4675 − 1.0530I 0
u = −1.73066 − 0.01255I
a = −1.72454 + 0.03435I
b = 1.50767 − 0.66940I
−17.4675 + 1.0530I 0
u = −1.73213 + 0.16868I
a = 1.84723 + 0.54357I
b = −1.46340 + 0.53545I
−16.6726 − 14.3095I 0
u = −1.73213 − 0.16868I
a = 1.84723 − 0.54357I
b = −1.46340 − 0.53545I
−16.6726 + 14.3095I 0
u = 1.78302 + 0.21856I
a = 1.55482 − 0.43122I
b = −1.41314 − 0.15182I
−17.8772 + 4.1906I 0
u = 1.78302 − 0.21856I
a = 1.55482 + 0.43122I
b = −1.41314 + 0.15182I
−17.8772 − 4.1906I 0
10
II. I
u
2
= hb + 3a + 1, 3a
2
+ 3a + 1, u
2
− u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u − 1
a
12
=
u
−u − 1
a
3
=
a
−3a − 1
a
9
=
−u
u
a
6
=
2a + 2
−3a − 2
a
2
=
3a
−3a
a
5
=
au + 3a + 2
−au − 4a − 2
a
10
=
−u
u
a
4
=
2au + 3a + u + 1
−2au − 5a − u − 2
a
1
=
−au + 3a + 1
au − 2a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10au − 5a +
11
3
u +
26
3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
12
(u
2
− u + 1)
2
c
2
, c
4
(u
2
+ u + 1)
2
c
3
9(9u
4
+ 9u
2
+ 1)
c
5
9(9u
4
− 9u
3
+ 3u + 1)
c
7
, c
8
(u
2
− u − 1)
2
c
9
u
4
c
10
, c
11
(u
2
+ u − 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
12
(y
2
+ y + 1)
2
c
3
81(9y
2
+ 9y + 1)
2
c
5
81(81y
4
− 81y
3
+ 72y
2
− 9y + 1)
c
7
, c
8
, c
10
c
11
(y
2
− 3y + 1)
2
c
9
y
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −0.500000 + 0.288675I
b = 0.500000 − 0.866025I
0.98696 − 2.02988I 11.99071 − 3.22749I
u = −0.618034
a = −0.500000 − 0.288675I
b = 0.500000 + 0.866025I
0.98696 + 2.02988I 11.99071 + 3.22749I
u = 1.61803
a = −0.500000 + 0.288675I
b = 0.500000 − 0.866025I
8.88264 − 2.02988I 9.00929 + 3.22749I
u = 1.61803
a = −0.500000 − 0.288675I
b = 0.500000 + 0.866025I
8.88264 + 2.02988I 9.00929 − 3.22749I
14
III. I
u
3
= hb + 1, a
2
− 4a + 6, u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
−1
a
8
=
1
−1
a
12
=
−1
0
a
3
=
a
−1
a
9
=
0
−1
a
6
=
−a + 1
1
a
2
=
1
0
a
5
=
−a + 1
−a + 2
a
10
=
1
−1
a
4
=
1
a − 2
a
1
=
−a + 3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
2
+ 2
c
2
, c
9
, c
10
c
11
(u − 1)
2
c
3
u
2
+ 2u + 3
c
5
u
2
− 2u + 3
c
6
, c
7
, c
8
(u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y + 2)
2
c
2
, c
6
, c
7
c
8
, c
9
, c
10
c
11
(y −1)
2
c
3
, c
5
y
2
+ 2y + 9
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 2.00000 + 1.41421I
b = −1.00000
8.22467 12.0000
u = −1.00000
a = 2.00000 − 1.41421I
b = −1.00000
8.22467 12.0000
18
IV. I
u
4
= hb − 1, a + 2, u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
−1
a
8
=
1
−1
a
12
=
−1
0
a
3
=
−2
1
a
9
=
0
−1
a
6
=
−1
1
a
2
=
−1
0
a
5
=
−1
0
a
10
=
1
−1
a
4
=
−1
0
a
1
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
c
2
, c
7
, c
8
c
9
u + 1
c
3
, c
5
, c
6
c
10
, c
11
u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −2.00000
b = 1.00000
3.28987 12.0000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
u(u
2
+ 2)(u
2
− u + 1)
2
(u
59
− 3u
58
+ ··· + 8u
2
+ 2)
c
2
((u − 1)
2
)(u + 1)(u
2
+ u + 1)
2
(u
59
− 4u
58
+ ··· − 19u + 3)
c
3
81(u − 1)(u
2
+ 2u + 3)(9u
4
+ 9u
2
+ 1)
· (9u
59
+ 48u
58
+ ··· − 422003u + 85781)
c
4
u(u
2
+ 2)(u
2
+ u + 1)
2
(u
59
− 3u
58
+ ··· + 8u
2
+ 2)
c
5
81(u − 1)(u
2
− 2u + 3)(9u
4
− 9u
3
+ 3u + 1)
· (9u
59
− 75u
58
+ ··· − 1270890u − 386003)
c
6
(u − 1)(u + 1)
2
(u
2
− u + 1)
2
(u
59
− 4u
58
+ ··· − 19u + 3)
c
7
, c
8
((u + 1)
3
)(u
2
− u − 1)
2
(u
59
− 6u
58
+ ··· − 41u + 9)
c
9
u
4
(u − 1)
2
(u + 1)(u
59
− 2u
58
+ ··· − 1152u + 432)
c
10
, c
11
((u − 1)
3
)(u
2
+ u − 1)
2
(u
59
− 6u
58
+ ··· − 41u + 9)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y(y + 2)
2
(y
2
+ y + 1)
2
(y
59
+ 63y
58
+ ··· − 32y −4)
c
2
, c
6
((y −1)
3
)(y
2
+ y + 1)
2
(y
59
− 44y
58
+ ··· + 355y −9)
c
3
6561(y −1)(y
2
+ 2y + 9)(9y
2
+ 9y + 1)
2
· (81y
59
+ 1944y
58
+ ··· + 16277317023y −7358379961)
c
5
6561(y −1)(y
2
+ 2y + 9)(81y
4
− 81y
3
+ 72y
2
− 9y + 1)
· (81y
59
− 5643y
58
+ ··· + 5638201231006y −148998316009)
c
7
, c
8
, c
10
c
11
((y −1)
3
)(y
2
− 3y + 1)
2
(y
59
− 76y
58
+ ··· + 1483y −81)
c
9
y
4
(y −1)
3
(y
59
+ 22y
58
+ ··· − 1627776y −186624)
24
