12a
0365
(K12a
0365
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 5 11 12 1 7 8 4
Solving Sequence
2,5
6 3
7,10
11 1 4 9 12 8
c
5
c
2
c
6
c
10
c
1
c
4
c
9
c
12
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.12893 × 10
45
u
69
+ 1.68277 × 10
46
u
68
+ ··· + 4.63662 × 10
44
b − 6.98652 × 10
45
,
5.16448 × 10
45
u
69
+ 1.76696 × 10
46
u
68
+ ··· + 4.63662 × 10
44
a − 1.03706 × 10
46
, u
70
+ 4u
69
+ ··· + 9u − 1i
I
u
2
= hu
2
+ b, −u
2
+ a + u, u
3
− u
2
+ 1i
I
u
3
= hb − a, a
2
+ a − 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 75 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
= h5.13 × 10
45
u
69
+ 1.68 × 10
46
u
68
+ · · · + 4.64 × 10
44
b − 6.99 × 10
45
, 5.16 ×
10
45
u
69
+1.77×10
46
u
68
+· · ·+4.64×10
44
a−1.04×10
46
, u
70
+4u
69
+· · ·+9u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
u
2
a
10
=
−11.1385u
69
− 38.1088u
68
+ ··· − 173.343u + 22.3667
−11.0618u
69
− 36.2931u
68
+ ··· − 165.547u + 15.0681
a
11
=
−10.4892u
69
− 34.4257u
68
+ ··· − 156.393u + 19.8877
−14.0832u
69
− 46.3168u
68
+ ··· − 196.252u + 18.2161
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−3.13298u
69
− 9.84215u
68
+ ··· − 17.5436u − 1.28092
1.91095u
69
+ 6.30251u
68
+ ··· + 32.7284u − 2.47449
a
9
=
−9.64324u
69
− 30.9560u
68
+ ··· − 143.863u + 19.4560
−13.0842u
69
− 43.4668u
68
+ ··· − 180.730u + 16.7111
a
12
=
4.89906u
69
+ 16.4905u
68
+ ··· + 65.1053u − 7.37396
4.33074u
69
+ 13.3350u
68
+ ··· + 61.2047u − 5.58668
a
8
=
−4.02982u
69
− 12.7973u
68
+ ··· − 53.5338u + 10.0666
−3.38116u
69
− 10.7655u
68
+ ··· − 42.5744u + 3.57024
(ii) Obstruction class = −1
(iii) Cusp Shapes = −128.394u
69
− 417.002u
68
+ ··· − 1794.20u + 180.894
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
70
+ 20u
69
+ ··· + 85u + 1
c
2
, c
5
u
70
+ 4u
69
+ ··· + 9u − 1
c
3
u
70
− 3u
69
+ ··· − 1882u − 203
c
4
u
70
− u
69
+ ··· − 1480438u − 582613
c
7
, c
8
, c
10
c
11
u
70
− 5u
69
+ ··· − 5u − 1
c
9
u
70
+ 4u
69
+ ··· + 8u + 4
c
12
u
70
+ 7u
69
+ ··· + 20u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
70
+ 64y
69
+ ··· − 5893y + 1
c
2
, c
5
y
70
− 20y
69
+ ··· − 85y + 1
c
3
y
70
+ 99y
69
+ ··· + 1211930y + 41209
c
4
y
70
+ 27y
69
+ ··· − 15150651595278y + 339437907769
c
7
, c
8
, c
10
c
11
y
70
− 87y
69
+ ··· − 151y + 1
c
9
y
70
+ 12y
69
+ ··· + 184y + 16
c
12
y
70
− 23y
69
+ ··· + 176y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821992 + 0.604536I
a = −0.532818 + 0.414673I
b = −0.120277 + 1.017190I
3.21297 + 2.35752I 0
u = −0.821992 − 0.604536I
a = −0.532818 − 0.414673I
b = −0.120277 − 1.017190I
3.21297 − 2.35752I 0
u = 0.936330 + 0.264637I
a = −0.896597 − 0.840149I
b = 0.665791 − 0.751664I
−2.22755 − 3.95507I 0
u = 0.936330 − 0.264637I
a = −0.896597 + 0.840149I
b = 0.665791 + 0.751664I
−2.22755 + 3.95507I 0
u = −0.894877 + 0.344146I
a = 0.584785 − 0.204131I
b = 0.118346 − 0.802002I
−1.90739 + 1.11321I 0
u = −0.894877 − 0.344146I
a = 0.584785 + 0.204131I
b = 0.118346 + 0.802002I
−1.90739 − 1.11321I 0
u = 0.853926 + 0.379140I
a = −1.07991 + 2.13533I
b = −0.768766 − 0.133800I
8.86997 − 3.71004I 5.02992 + 4.95815I
u = 0.853926 − 0.379140I
a = −1.07991 − 2.13533I
b = −0.768766 + 0.133800I
8.86997 + 3.71004I 5.02992 − 4.95815I
u = 0.076050 + 0.910271I
a = 0.786878 + 0.417494I
b = −1.286790 − 0.266397I
12.21590 + 5.26874I 9.05075 − 4.23813I
u = 0.076050 − 0.910271I
a = 0.786878 − 0.417494I
b = −1.286790 + 0.266397I
12.21590 − 5.26874I 9.05075 + 4.23813I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.053090 + 0.329534I
a = 0.301987 + 0.839033I
b = −0.884319 + 0.768012I
0.05205 − 7.60424I 0
u = 1.053090 − 0.329534I
a = 0.301987 − 0.839033I
b = −0.884319 − 0.768012I
0.05205 + 7.60424I 0
u = −0.873719
a = 0.0354661
b = 0.465987
−1.43825 −7.21730
u = 0.839383 + 0.766541I
a = 1.97243 + 0.15164I
b = −1.28254 + 0.70957I
3.50192 − 1.96491I 0
u = 0.839383 − 0.766541I
a = 1.97243 − 0.15164I
b = −1.28254 − 0.70957I
3.50192 + 1.96491I 0
u = −1.130380 + 0.210061I
a = −0.464632 − 0.272711I
b = −0.451919 + 0.228098I
−0.745084 − 0.635310I 0
u = −1.130380 − 0.210061I
a = −0.464632 + 0.272711I
b = −0.451919 − 0.228098I
−0.745084 + 0.635310I 0
u = 0.879194 + 0.755731I
a = −2.58309 + 2.90548I
b = −0.13084 − 3.76242I
4.28859 − 2.86154I 0
u = 0.879194 − 0.755731I
a = −2.58309 − 2.90548I
b = −0.13084 + 3.76242I
4.28859 + 2.86154I 0
u = −0.818848 + 0.830702I
a = 1.51994 − 0.93351I
b = −1.068180 + 0.239833I
4.67474 − 1.95463I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818848 − 0.830702I
a = 1.51994 + 0.93351I
b = −1.068180 − 0.239833I
4.67474 + 1.95463I 0
u = 0.756256 + 0.888290I
a = −0.908087 − 0.235986I
b = 0.978137 + 0.193385I
7.15283 − 0.79673I 0
u = 0.756256 − 0.888290I
a = −0.908087 + 0.235986I
b = 0.978137 − 0.193385I
7.15283 + 0.79673I 0
u = −0.779738 + 0.882642I
a = −1.34956 + 0.96896I
b = 1.40703 − 0.65492I
8.05847 − 6.46660I 0
u = −0.779738 − 0.882642I
a = −1.34956 − 0.96896I
b = 1.40703 + 0.65492I
8.05847 + 6.46660I 0
u = 0.921897 + 0.750500I
a = −1.04326 − 1.35120I
b = 1.282040 + 0.357501I
3.24664 − 3.77981I 0
u = 0.921897 − 0.750500I
a = −1.04326 + 1.35120I
b = 1.282040 − 0.357501I
3.24664 + 3.77981I 0
u = 0.890245 + 0.790410I
a = 2.42222 − 2.22983I
b = 0.02417 + 3.67851I
12.73530 − 2.97097I 0
u = 0.890245 − 0.790410I
a = 2.42222 + 2.22983I
b = 0.02417 − 3.67851I
12.73530 + 2.97097I 0
u = −0.795789 + 0.142506I
a = −1.53396 − 2.52646I
b = −1.17773 − 2.40528I
7.52169 + 0.34716I 21.0536 + 3.3715I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.795789 − 0.142506I
a = −1.53396 + 2.52646I
b = −1.17773 + 2.40528I
7.52169 − 0.34716I 21.0536 − 3.3715I
u = 1.140890 + 0.364834I
a = 0.103618 − 0.905249I
b = 1.175310 − 0.699942I
8.58977 − 9.64731I 0
u = 1.140890 − 0.364834I
a = 0.103618 + 0.905249I
b = 1.175310 + 0.699942I
8.58977 + 9.64731I 0
u = −0.879597 + 0.814650I
a = −1.56862 + 1.07443I
b = 0.986495 + 0.292630I
6.96123 + 3.17768I 0
u = −0.879597 − 0.814650I
a = −1.56862 − 1.07443I
b = 0.986495 − 0.292630I
6.96123 − 3.17768I 0
u = −0.765989 + 0.932811I
a = 1.26151 − 1.07522I
b = −1.77664 + 0.92423I
17.3945 − 9.1380I 0
u = −0.765989 − 0.932811I
a = 1.26151 + 1.07522I
b = −1.77664 − 0.92423I
17.3945 + 9.1380I 0
u = −0.861076 + 0.848477I
a = −0.859319 + 0.438890I
b = 1.26257 − 0.76714I
16.2859 − 0.4977I 0
u = −0.861076 − 0.848477I
a = −0.859319 − 0.438890I
b = 1.26257 + 0.76714I
16.2859 + 0.4977I 0
u = −0.908549 + 0.804614I
a = 1.43278 − 0.30075I
b = −1.103350 + 0.163447I
6.87034 + 2.88148I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.908549 − 0.804614I
a = 1.43278 + 0.30075I
b = −1.103350 − 0.163447I
6.87034 − 2.88148I 0
u = 0.744970 + 0.985585I
a = 0.647817 + 0.473956I
b = −1.163770 − 0.687098I
16.4531 − 0.4058I 0
u = 0.744970 − 0.985585I
a = 0.647817 − 0.473956I
b = −1.163770 + 0.687098I
16.4531 + 0.4058I 0
u = 0.069642 + 0.760028I
a = −0.793095 − 0.598689I
b = 0.859741 + 0.405238I
3.25439 + 3.89128I 8.22204 − 6.04817I
u = 0.069642 − 0.760028I
a = −0.793095 + 0.598689I
b = 0.859741 − 0.405238I
3.25439 − 3.89128I 8.22204 + 6.04817I
u = −0.958273 + 0.787843I
a = −1.80471 + 0.55498I
b = 1.167160 + 0.384223I
4.24350 + 8.00749I 0
u = −0.958273 − 0.787843I
a = −1.80471 − 0.55498I
b = 1.167160 − 0.384223I
4.24350 − 8.00749I 0
u = −0.939681 + 0.820477I
a = 1.49590 − 1.03839I
b = −1.084500 − 0.834712I
16.0406 + 6.7093I 0
u = −0.939681 − 0.820477I
a = 1.49590 + 1.03839I
b = −1.084500 + 0.834712I
16.0406 − 6.7093I 0
u = 0.715806 + 0.197898I
a = 1.90591 + 0.45104I
b = −0.684371 + 0.426921I
1.024240 − 0.486676I 5.73519 + 8.27485I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715806 − 0.197898I
a = 1.90591 − 0.45104I
b = −0.684371 − 0.426921I
1.024240 + 0.486676I 5.73519 − 8.27485I
u = −0.731580 + 0.051178I
a = 0.44870 + 2.26858I
b = 0.01502 + 2.39231I
−0.138452 + 0.200334I 4.9583 + 27.7973I
u = −0.731580 − 0.051178I
a = 0.44870 − 2.26858I
b = 0.01502 − 2.39231I
−0.138452 − 0.200334I 4.9583 − 27.7973I
u = −1.250450 + 0.234036I
a = 0.590103 + 0.537183I
b = 0.859854 + 0.006608I
7.57482 − 1.28932I 0
u = −1.250450 − 0.234036I
a = 0.590103 − 0.537183I
b = 0.859854 − 0.006608I
7.57482 + 1.28932I 0
u = −1.001820 + 0.796995I
a = 1.91846 − 0.82073I
b = −1.44365 − 0.79366I
7.3655 + 12.6957I 0
u = −1.001820 − 0.796995I
a = 1.91846 + 0.82073I
b = −1.44365 + 0.79366I
7.3655 − 12.6957I 0
u = 1.012350 + 0.795855I
a = 1.031530 + 0.756442I
b = −0.955690 + 0.405302I
6.36559 − 5.43747I 0
u = 1.012350 − 0.795855I
a = 1.031530 − 0.756442I
b = −0.955690 − 0.405302I
6.36559 + 5.43747I 0
u = −1.033470 + 0.811620I
a = −1.97244 + 1.02030I
b = 1.74303 + 1.08840I
16.5467 + 15.5606I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.033470 − 0.811620I
a = −1.97244 − 1.02030I
b = 1.74303 − 1.08840I
16.5467 − 15.5606I 0
u = 0.597160 + 0.280730I
a = 0.35750 − 2.20071I
b = 0.268738 + 0.108233I
1.24480 − 1.64965I 7.01663 + 7.54846I
u = 0.597160 − 0.280730I
a = 0.35750 + 2.20071I
b = 0.268738 − 0.108233I
1.24480 + 1.64965I 7.01663 − 7.54846I
u = 1.069430 + 0.833772I
a = −1.142940 − 0.662361I
b = 1.013930 − 0.881403I
15.4304 − 6.2393I 0
u = 1.069430 − 0.833772I
a = −1.142940 + 0.662361I
b = 1.013930 + 0.881403I
15.4304 + 6.2393I 0
u = 0.345521 + 0.465734I
a = −1.78206 + 0.64019I
b = 1.51987 − 0.09297I
10.36090 + 0.46448I 7.45738 + 2.55790I
u = 0.345521 − 0.465734I
a = −1.78206 − 0.64019I
b = 1.51987 + 0.09297I
10.36090 − 0.46448I 7.45738 − 2.55790I
u = 0.049655 + 0.436764I
a = 1.29855 + 1.08613I
b = −0.333410 − 0.509182I
0.274835 + 1.373660I 2.74778 − 4.32482I
u = 0.049655 − 0.436764I
a = 1.29855 − 1.08613I
b = −0.333410 + 0.509182I
0.274835 − 1.373660I 2.74778 + 4.32482I
u = 0.114333
a = 5.43350
b = −0.726957
1.36710 7.44230
11
II. I
u
2
= hu
2
+ b, −u
2
+ a + u, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
7
=
−u
2
+ 1
u
2
a
10
=
u
2
− u
−u
2
a
11
=
2u
2
− u − 1
−2u
2
a
1
=
u
2
− 1
−u
2
a
4
=
u + 1
u
2
− u − 1
a
9
=
2u
2
− u − 1
−2u
2
a
12
=
u
2
− 1
−u
2
a
8
=
u
2
− u
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
+ 7u + 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
, c
4
, c
6
u
3
+ u
2
+ 2u + 1
c
5
u
3
− u
2
+ 1
c
7
, c
8
, c
9
(u + 1)
3
c
10
, c
11
(u − 1)
3
c
12
u
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
y
3
− y
2
+ 2y −1
c
7
, c
8
, c
9
c
10
, c
11
(y −1)
3
c
12
y
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.662359 + 0.562280I
b = −0.215080 − 1.307140I
4.66906 − 2.82812I 7.71191 + 2.59975I
u = 0.877439 − 0.744862I
a = −0.662359 − 0.562280I
b = −0.215080 + 1.307140I
4.66906 + 2.82812I 7.71191 − 2.59975I
u = −0.754878
a = 1.32472
b = −0.569840
0.531480 −4.42380
15
III. I
u
3
= hb − a, a
2
+ a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
7
=
0
1
a
10
=
a
a
a
11
=
a
0
a
1
=
−1
−1
a
4
=
−a + 2
−a + 1
a
9
=
a
a
a
12
=
−a + 1
−a
a
8
=
−a + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
2
c
3
, c
4
, c
10
c
11
u
2
+ u − 1
c
5
, c
6
(u + 1)
2
c
7
, c
8
u
2
− u − 1
c
9
u
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
12
(y −1)
2
c
3
, c
4
, c
7
c
8
, c
10
, c
11
y
2
− 3y + 1
c
9
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.618034
b = 0.618034
−0.657974 5.00000
u = −1.00000
a = −1.61803
b = −1.61803
7.23771 5.00000
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
3
− u
2
+ 2u − 1)(u
70
+ 20u
69
+ ··· + 85u + 1)
c
2
((u − 1)
2
)(u
3
+ u
2
− 1)(u
70
+ 4u
69
+ ··· + 9u − 1)
c
3
(u
2
+ u − 1)(u
3
+ u
2
+ 2u + 1)(u
70
− 3u
69
+ ··· − 1882u − 203)
c
4
(u
2
+ u − 1)(u
3
+ u
2
+ 2u + 1)(u
70
− u
69
+ ··· − 1480438u − 582613)
c
5
((u + 1)
2
)(u
3
− u
2
+ 1)(u
70
+ 4u
69
+ ··· + 9u − 1)
c
6
((u + 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
70
+ 20u
69
+ ··· + 85u + 1)
c
7
, c
8
((u + 1)
3
)(u
2
− u − 1)(u
70
− 5u
69
+ ··· − 5u − 1)
c
9
u
2
(u + 1)
3
(u
70
+ 4u
69
+ ··· + 8u + 4)
c
10
, c
11
((u − 1)
3
)(u
2
+ u − 1)(u
70
− 5u
69
+ ··· − 5u − 1)
c
12
u
3
(u − 1)
2
(u
70
+ 7u
69
+ ··· + 20u + 8)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y −1)
2
)(y
3
+ 3y
2
+ 2y −1)(y
70
+ 64y
69
+ ··· − 5893y + 1)
c
2
, c
5
((y −1)
2
)(y
3
− y
2
+ 2y −1)(y
70
− 20y
69
+ ··· − 85y + 1)
c
3
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y −1)
· (y
70
+ 99y
69
+ ··· + 1211930y + 41209)
c
4
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y −1)
· (y
70
+ 27y
69
+ ··· − 15150651595278y + 339437907769)
c
7
, c
8
, c
10
c
11
((y −1)
3
)(y
2
− 3y + 1)(y
70
− 87y
69
+ ··· − 151y + 1)
c
9
y
2
(y −1)
3
(y
70
+ 12y
69
+ ··· + 184y + 16)
c
12
y
3
(y −1)
2
(y
70
− 23y
69
+ ··· + 176y + 64)
21
