12a
1017
(K12a
1017
)
A knot diagram
1
Linearized knot diagam
4 6 1 10 9 11 12 3 5 2 7 8
Solving Sequence
4,10 2,5
11 1 3 9 6 7 8 12
c
4
c
10
c
1
c
3
c
9
c
5
c
6
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.60368 × 10
56
u
58
+ 4.19299 × 10
56
u
57
+ ··· + 1.57047 × 10
57
b + 1.44031 × 10
57
,
− 1.44721 × 10
58
u
58
+ 2.32648 × 10
58
u
57
+ ··· + 1.72751 × 10
58
a − 2.18987 × 10
58
, u
59
− 2u
58
+ ··· + 2u − 1i
I
u
2
= hb + 1, −6u
4
− u
3
− 4u
2
+ 11a − 6u − 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 64 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
= h−2.60×10
56
u
58
+4.19×10
56
u
57
+· · ·+1.57×10
57
b+1.44×10
57
, −1.45×
10
58
u
58
+2.33×10
58
u
57
+· · ·+1.73×10
58
a−2.19×10
58
, u
59
−2u
58
+· · ·+2u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
0.837744u
58
− 1.34673u
57
+ ··· + 9.36260u + 1.26764
0.165790u
58
− 0.266990u
57
+ ··· − 0.250227u − 0.917125
a
5
=
1
−u
2
a
11
=
−1.37006u
58
+ 2.70687u
57
+ ··· − 2.20419u − 7.53648
0.323082u
58
− 0.735433u
57
+ ··· + 0.636173u + 0.712700
a
1
=
1.00353u
58
− 1.61372u
57
+ ··· + 9.11237u + 0.350517
0.165790u
58
− 0.266990u
57
+ ··· − 0.250227u − 0.917125
a
3
=
0.813781u
58
− 1.27902u
57
+ ··· + 9.23409u + 1.12697
0.101081u
58
− 0.176699u
57
+ ··· − 0.139831u − 0.934603
a
9
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
1.22085u
58
− 1.69130u
57
+ ··· + 1.86963u + 5.41585
−0.341950u
58
+ 0.451068u
57
+ ··· + 0.714485u − 0.813658
a
8
=
−1.10578u
58
+ 1.81302u
57
+ ··· − 8.88249u − 6.38263
0.522951u
58
− 1.01970u
57
+ ··· − 0.297256u + 0.859688
a
12
=
−0.815570u
58
+ 1.08491u
57
+ ··· + 7.19499u − 5.10912
0.485858u
58
− 0.909085u
57
+ ··· − 1.03362u + 0.314960
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.95860u
58
− 4.62866u
57
+ ··· − 1.56836u + 1.88588
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
59
− 6u
58
+ ··· − 222u − 121
c
2
u
59
− 5u
58
+ ··· − 9856u − 3872
c
4
, c
5
, c
9
u
59
− 2u
58
+ ··· + 2u − 1
c
6
, c
7
, c
11
c
12
u
59
− 2u
58
+ ··· − 2u − 1
c
8
11(11u
59
+ 7u
58
+ ··· − 474357u − 87053)
c
10
11(11u
59
+ 48u
58
+ ··· − 267960u + 42881)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
59
− 56y
58
+ ··· + 212150y −14641
c
2
y
59
+ 33y
58
+ ··· − 70687232y −14992384
c
4
, c
5
, c
9
y
59
+ 60y
58
+ ··· − 8y −1
c
6
, c
7
, c
11
c
12
y
59
− 72y
58
+ ··· − 8y −1
c
8
121(121y
59
+ 4725y
58
+ ··· + 3.57051 × 10
10
y −7.57822 × 10
9
)
c
10
121(121y
59
− 6660y
58
+ ··· + 8.46566 × 10
10
y −1.83878 × 10
9
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796037 + 0.604484I
a = −0.74747 + 1.39314I
b = 1.49990 − 0.41719I
−15.3122 + 10.3381I 0
u = 0.796037 − 0.604484I
a = −0.74747 − 1.39314I
b = 1.49990 + 0.41719I
−15.3122 − 10.3381I 0
u = 0.198490 + 0.977565I
a = 0.562353 + 0.184287I
b = 0.471286 − 0.024219I
−0.98563 + 1.68469I 0
u = 0.198490 − 0.977565I
a = 0.562353 − 0.184287I
b = 0.471286 + 0.024219I
−0.98563 − 1.68469I 0
u = 0.858738 + 0.528700I
a = −1.152010 + 0.399429I
b = 1.45085 + 0.23811I
−15.0363 − 4.8637I 0
u = 0.858738 − 0.528700I
a = −1.152010 − 0.399429I
b = 1.45085 − 0.23811I
−15.0363 + 4.8637I 0
u = −0.817032 + 0.626568I
a = −0.648949 − 1.133500I
b = 1.38602 + 0.29741I
−6.17225 − 7.56398I 0
u = −0.817032 − 0.626568I
a = −0.648949 + 1.133500I
b = 1.38602 − 0.29741I
−6.17225 + 7.56398I 0
u = −0.893731 + 0.562783I
a = −0.876424 − 0.537932I
b = 1.347250 − 0.074003I
−5.89406 + 1.87040I 0
u = −0.893731 − 0.562783I
a = −0.876424 + 0.537932I
b = 1.347250 + 0.074003I
−5.89406 − 1.87040I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.874153 + 0.628437I
a = −0.661838 + 0.795197I
b = 1.311200 − 0.117019I
−3.14430 + 2.95119I 0
u = 0.874153 − 0.628437I
a = −0.661838 − 0.795197I
b = 1.311200 + 0.117019I
−3.14430 − 2.95119I 0
u = −0.773705
a = −0.220081
b = 0.601717
−3.27963 1.19980
u = −0.396789 + 1.233380I
a = 0.219506 − 0.235740I
b = 0.709981 − 0.143756I
−6.97611 − 4.18850I 0
u = −0.396789 − 1.233380I
a = 0.219506 + 0.235740I
b = 0.709981 + 0.143756I
−6.97611 + 4.18850I 0
u = 0.484963 + 0.479670I
a = 0.08284 − 1.77415I
b = −0.303027 + 1.146960I
−9.50379 + 4.88030I −7.71303 − 6.76491I
u = 0.484963 − 0.479670I
a = 0.08284 + 1.77415I
b = −0.303027 − 1.146960I
−9.50379 − 4.88030I −7.71303 + 6.76491I
u = −0.183341 + 0.604919I
a = 1.00666 + 1.24021I
b = −1.51219 − 0.51372I
−13.31950 − 1.94537I −13.47697 + 3.50593I
u = −0.183341 − 0.604919I
a = 1.00666 − 1.24021I
b = −1.51219 + 0.51372I
−13.31950 + 1.94537I −13.47697 − 3.50593I
u = −0.474884 + 0.413829I
a = 0.19300 + 1.46597I
b = −0.208163 − 0.850495I
−1.11164 − 3.54239I −5.29217 + 9.29513I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.474884 − 0.413829I
a = 0.19300 − 1.46597I
b = −0.208163 + 0.850495I
−1.11164 + 3.54239I −5.29217 − 9.29513I
u = 0.06846 + 1.41970I
a = 1.51433 − 1.48737I
b = −0.588804 − 0.059904I
−14.7804 − 0.1036I 0
u = 0.06846 − 1.41970I
a = 1.51433 + 1.48737I
b = −0.588804 + 0.059904I
−14.7804 + 0.1036I 0
u = −0.08071 + 1.43356I
a = 0.457428 + 1.119880I
b = −0.482493 − 0.333450I
−6.79984 − 0.65977I 0
u = −0.08071 − 1.43356I
a = 0.457428 − 1.119880I
b = −0.482493 + 0.333450I
−6.79984 + 0.65977I 0
u = 0.433200 + 0.354869I
a = 2.49189 + 0.41018I
b = −0.334250 − 0.608931I
−9.24314 − 1.69409I −6.45770 − 2.18401I
u = 0.433200 − 0.354869I
a = 2.49189 − 0.41018I
b = −0.334250 + 0.608931I
−9.24314 + 1.69409I −6.45770 + 2.18401I
u = 0.481378 + 0.284287I
a = 0.331714 − 0.880870I
b = 0.012838 + 0.449350I
0.847712 + 0.957954I 3.55490 − 3.49861I
u = 0.481378 − 0.284287I
a = 0.331714 + 0.880870I
b = 0.012838 − 0.449350I
0.847712 − 0.957954I 3.55490 + 3.49861I
u = 0.167534 + 0.526581I
a = 0.549164 − 1.250740I
b = −1.304810 + 0.390671I
−4.53243 + 1.53708I −14.0615 − 4.6733I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.167534 − 0.526581I
a = 0.549164 + 1.250740I
b = −1.304810 − 0.390671I
−4.53243 − 1.53708I −14.0615 + 4.6733I
u = 0.12471 + 1.45410I
a = 0.004794 − 0.718738I
b = −0.277273 + 0.839860I
−4.85539 + 3.02727I 0
u = 0.12471 − 1.45410I
a = 0.004794 + 0.718738I
b = −0.277273 − 0.839860I
−4.85539 − 3.02727I 0
u = −0.02219 + 1.47985I
a = −1.184660 + 0.716156I
b = −1.270660 − 0.208426I
−7.84581 − 1.05414I 0
u = −0.02219 − 1.47985I
a = −1.184660 − 0.716156I
b = −1.270660 + 0.208426I
−7.84581 + 1.05414I 0
u = −0.13458 + 1.48905I
a = −0.212419 + 0.736437I
b = −0.364158 − 1.264080I
−7.38067 − 5.69306I 0
u = −0.13458 − 1.48905I
a = −0.212419 − 0.736437I
b = −0.364158 + 1.264080I
−7.38067 + 5.69306I 0
u = 0.13963 + 1.50988I
a = −0.312693 − 0.771821I
b = −0.40912 + 1.57743I
−16.0816 + 7.1054I 0
u = 0.13963 − 1.50988I
a = −0.312693 + 0.771821I
b = −0.40912 − 1.57743I
−16.0816 − 7.1054I 0
u = −0.324223 + 0.354209I
a = 1.72152 + 0.17031I
b = −0.192221 + 0.236728I
−1.22883 + 0.71007I −5.89409 − 0.17363I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.324223 − 0.354209I
a = 1.72152 − 0.17031I
b = −0.192221 − 0.236728I
−1.22883 − 0.71007I −5.89409 + 0.17363I
u = 0.04032 + 1.51980I
a = −0.376465 − 0.573934I
b = −1.66993 + 0.60898I
−11.34980 + 2.24363I 0
u = 0.04032 − 1.51980I
a = −0.376465 + 0.573934I
b = −1.66993 − 0.60898I
−11.34980 − 2.24363I 0
u = −0.04376 + 1.53939I
a = −0.162577 + 0.558268I
b = −1.96174 − 0.79822I
19.0042 − 2.7199I 0
u = −0.04376 − 1.53939I
a = −0.162577 − 0.558268I
b = −1.96174 + 0.79822I
19.0042 + 2.7199I 0
u = −0.413308
a = 6.18719
b = −1.24773
−11.3722 2.89400
u = 0.26816 + 1.57009I
a = 0.353918 + 1.205710I
b = 1.60951 − 0.53863I
17.0282 + 14.2654I 0
u = 0.26816 − 1.57009I
a = 0.353918 − 1.205710I
b = 1.60951 + 0.53863I
17.0282 − 14.2654I 0
u = −0.26921 + 1.57903I
a = 0.349462 − 1.077470I
b = 1.52595 + 0.44331I
−13.4198 − 11.5636I 0
u = −0.26921 − 1.57903I
a = 0.349462 + 1.077470I
b = 1.52595 − 0.44331I
−13.4198 + 11.5636I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31035 + 1.57601I
a = 0.005917 + 0.764911I
b = 1.51814 + 0.02689I
17.5634 − 0.5001I 0
u = 0.31035 − 1.57601I
a = 0.005917 − 0.764911I
b = 1.51814 − 0.02689I
17.5634 + 0.5001I 0
u = 0.27658 + 1.59112I
a = 0.306850 + 0.928705I
b = 1.45225 − 0.31276I
−10.47530 + 7.16280I 0
u = 0.27658 − 1.59112I
a = 0.306850 − 0.928705I
b = 1.45225 + 0.31276I
−10.47530 − 7.16280I 0
u = −0.29657 + 1.59268I
a = 0.174916 − 0.817280I
b = 1.45444 + 0.14492I
−13.01790 − 2.55081I 0
u = −0.29657 − 1.59268I
a = 0.174916 + 0.817280I
b = 1.45444 − 0.14492I
−13.01790 + 2.55081I 0
u = −0.149750 + 0.332749I
a = −0.60011 + 2.68313I
b = −1.005990 − 0.128622I
−1.78637 − 0.56805I −5.68333 − 3.31211I
u = −0.149750 − 0.332749I
a = −0.60011 − 2.68313I
b = −1.005990 + 0.128622I
−1.78637 + 0.56805I −5.68333 + 3.31211I
u = 0.315139
a = 7.79706
b = −1.08358
−2.97694 19.5050
10
II. I
u
2
= hb + 1, −6u
4
− u
3
− 4u
2
+ 11 a − 6u − 2, u
5
− u
4
+ 2 u
3
− u
2
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
0.545455u
4
+ 0.0909091u
3
+ ··· + 0.545455u + 0.181818
−1
a
5
=
1
−u
2
a
11
=
−0.280992u
4
− 0.0165289u
3
+ ··· + 0.0826446u − 0.487603
0.636364u
4
− 0.727273u
3
+ ··· + 0.636364u + 0.545455
a
1
=
0.545455u
4
+ 0.0909091u
3
+ ··· + 0.545455u − 0.818182
−1
a
3
=
0.545455u
4
+ 0.0909091u
3
+ ··· + 0.545455u + 0.181818
−1
a
9
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−0.157025u
4
+ 0.0495868u
3
+ ··· − 0.247934u + 0.462810
0.0909091u
4
+ 0.181818u
3
+ ··· + 0.0909091u + 0.363636
a
8
=
0.0991736u
4
− 0.347107u
3
+ ··· − 1.26446u − 0.239669
0.363636u
4
+ 0.727273u
3
+ ··· + 0.363636u + 0.454545
a
12
=
−0.752066u
4
+ 0.132231u
3
+ ··· + 0.338843u − 1.09917
0.909091u
4
− 1.18182u
3
+ ··· − 0.0909091u + 0.636364
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
121
u
4
+
619
121
u
3
−
527
121
u
2
+
414
121
u −
1523
121
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
u
5
c
3
(u + 1)
5
c
4
, c
5
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
6
, c
7
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
8
11(11u
5
− 2u
4
+ 6u
3
+ u
2
+ 1)
c
9
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
10
11(11u
5
+ 13u
4
− 3u
2
+ u + 1)
c
11
, c
12
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
5
c
2
y
5
c
4
, c
5
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
7
, c
11
c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
121(121y
5
+ 128y
4
+ 40y
3
+ 3y
2
− 2y −1)
c
10
121(121y
5
− 169y
4
+ 100y
3
− 35y
2
+ 7y −1)
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −0.146090 + 0.562510I
b = −1.00000
−1.97403 − 1.53058I −7.98225 + 3.82841I
u = −0.339110 − 0.822375I
a = −0.146090 − 0.562510I
b = −1.00000
−1.97403 + 1.53058I −7.98225 − 3.82841I
u = 0.766826
a = 1.04351
b = −1.00000
−4.04602 −10.2290
u = 0.455697 + 1.200150I
a = −0.012026 − 0.507727I
b = −1.00000
−7.51750 + 4.40083I −15.2587 − 5.5869I
u = 0.455697 − 1.200150I
a = −0.012026 + 0.507727I
b = −1.00000
−7.51750 − 4.40083I −15.2587 + 5.5869I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
59
− 6u
58
+ ··· − 222u − 121)
c
2
u
5
(u
59
− 5u
58
+ ··· − 9856u − 3872)
c
3
((u + 1)
5
)(u
59
− 6u
58
+ ··· − 222u − 121)
c
4
, c
5
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
59
− 2u
58
+ ··· + 2u − 1)
c
6
, c
7
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
59
− 2u
58
+ ··· − 2u − 1)
c
8
121(11u
5
− 2u
4
+ 6u
3
+ u
2
+ 1)
· (11u
59
+ 7u
58
+ ··· − 474357u − 87053)
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
59
− 2u
58
+ ··· + 2u − 1)
c
10
121(11u
5
+ 13u
4
− 3u
2
+ u + 1)
· (11u
59
+ 48u
58
+ ··· − 267960u + 42881)
c
11
, c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
59
− 2u
58
+ ··· − 2u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
5
)(y
59
− 56y
58
+ ··· + 212150y −14641)
c
2
y
5
(y
59
+ 33y
58
+ ··· − 7.06872 × 10
7
y −1.49924 × 10
7
)
c
4
, c
5
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
59
+ 60y
58
+ ··· − 8y −1)
c
6
, c
7
, c
11
c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
59
− 72y
58
+ ··· − 8y −1)
c
8
14641(121y
5
+ 128y
4
+ 40y
3
+ 3y
2
− 2y −1)
· (121y
59
+ 4725y
58
+ ··· + 35705105211y −7578224809)
c
10
14641(121y
5
− 169y
4
+ 100y
3
− 35y
2
+ 7y −1)
· (121y
59
− 6660y
58
+ ··· + 84656570160y −1838780161)
16
