12a
0367
(K12a
0367
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 11 12 5 4 1 7 8
Solving Sequence
6,11
7 12
3,8
2 1 5 9 10 4
c
6
c
11
c
7
c
2
c
1
c
5
c
8
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.26039 × 10
20
u
71
− 3.31809 × 10
22
u
70
+ ··· + 4.33870 × 10
22
b + 1.79186 × 10
22
,
− 8.36919 × 10
22
u
71
+ 1.25008 × 10
23
u
70
+ ··· + 8.67739 × 10
22
a + 3.24699 × 10
22
, u
72
− 2u
71
+ ··· + 2u + 1i
I
u
2
= hb − 1, a
2
− 2a + 2u − 3, u
2
− u − 1i
I
u
3
= hb + 1, a + 1, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 78 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−5.26×10
20
u
71
−3.32×10
22
u
70
+· · ·+4.34×10
22
b+1.79×10
22
, −8.37×
10
22
u
71
+1.25×10
23
u
70
+· · ·+8.68×10
22
a+3.25×10
22
, u
72
−2u
71
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
0.964482u
71
− 1.44061u
70
+ ··· − 11.9876u − 0.374190
0.0121244u
71
+ 0.764766u
70
+ ··· + 0.453521u − 0.412996
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
0.976607u
71
− 0.675847u
70
+ ··· − 11.5341u − 0.787186
0.0121244u
71
+ 0.764766u
70
+ ··· + 0.453521u − 0.412996
a
1
=
u
3
− 2u
u
5
− 3u
3
+ u
a
5
=
−1.98741u
71
+ 1.11158u
70
+ ··· + 14.3859u + 3.65867
−0.926705u
71
+ 0.404836u
70
+ ··· + 1.82730u + 0.532714
a
9
=
0.472718u
71
− 1.08136u
70
+ ··· − 16.3593u − 1.33874
−1.10315u
71
+ 1.20031u
70
+ ··· + 2.20486u + 0.947164
a
10
=
u
7
− 4u
5
+ 4u
3
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
4
=
−1.55989u
71
+ 0.727017u
70
+ ··· + 13.9611u + 3.63430
−0.566397u
71
+ 0.322301u
70
+ ··· − 0.405449u − 0.412002
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
124925391140869705539849
43386961394563898337977
u
71
+
155786602228314171185371
43386961394563898337977
u
70
+ ··· +
536149016094843518284893
43386961394563898337977
u −
597134730501655502761745
43386961394563898337977
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 37u
71
+ ··· + 29u + 1
c
2
, c
5
u
72
+ 3u
71
+ ··· + 7u + 1
c
3
, c
4
, c
9
u
72
− u
71
+ ··· − 12u − 4
c
6
, c
7
, c
11
c
12
u
72
− 2u
71
+ ··· + 2u + 1
c
8
u
72
+ 3u
71
+ ··· + 1492u + 220
c
10
u
72
− 20u
71
+ ··· − 348u + 113
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
+ 3y
71
+ ··· − 197y + 1
c
2
, c
5
y
72
− 37y
71
+ ··· − 29y + 1
c
3
, c
4
, c
9
y
72
− 67y
71
+ ··· − 16y + 16
c
6
, c
7
, c
11
c
12
y
72
− 84y
71
+ ··· − 20y + 1
c
8
y
72
− 7y
71
+ ··· − 402704y + 48400
c
10
y
72
− 12y
71
+ ··· − 272524y + 12769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.928218 + 0.309234I
a = −0.354302 + 0.192132I
b = −1.065700 + 0.515640I
−7.24752 + 4.65448I 0
u = 0.928218 − 0.309234I
a = −0.354302 − 0.192132I
b = −1.065700 − 0.515640I
−7.24752 − 4.65448I 0
u = −0.737630 + 0.531689I
a = −0.70377 − 2.08141I
b = −1.166590 + 0.587970I
−5.52989 + 11.86830I 0
u = −0.737630 − 0.531689I
a = −0.70377 + 2.08141I
b = −1.166590 − 0.587970I
−5.52989 − 11.86830I 0
u = −0.884804 + 0.189140I
a = 0.504034 + 0.110912I
b = 0.931780 + 0.416732I
−2.20323 − 1.64389I 0
u = −0.884804 − 0.189140I
a = 0.504034 − 0.110912I
b = 0.931780 − 0.416732I
−2.20323 + 1.64389I 0
u = 0.883338 + 0.137471I
a = −0.750844 + 0.235422I
b = −0.381393 − 0.511313I
−5.31297 + 0.37168I −12.00000 + 0.I
u = 0.883338 − 0.137471I
a = −0.750844 − 0.235422I
b = −0.381393 + 0.511313I
−5.31297 − 0.37168I −12.00000 + 0.I
u = 0.690814 + 0.522826I
a = 0.56315 − 2.15893I
b = 1.099150 + 0.589092I
0.02673 − 8.09347I −12.0000 + 9.2851I
u = 0.690814 − 0.522826I
a = 0.56315 + 2.15893I
b = 1.099150 − 0.589092I
0.02673 + 8.09347I −12.0000 − 9.2851I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.678297 + 0.515178I
a = 0.977292 + 0.542744I
b = −0.295256 − 0.854652I
−2.93335 + 6.55153I −14.6691 − 6.1676I
u = −0.678297 − 0.515178I
a = 0.977292 − 0.542744I
b = −0.295256 + 0.854652I
−2.93335 − 6.55153I −14.6691 + 6.1676I
u = −0.630548 + 0.470751I
a = −0.34238 − 2.38082I
b = −1.003340 + 0.528804I
−1.31023 + 3.89736I −15.2781 − 4.8812I
u = −0.630548 − 0.470751I
a = −0.34238 + 2.38082I
b = −1.003340 − 0.528804I
−1.31023 − 3.89736I −15.2781 + 4.8812I
u = −0.669262 + 0.404635I
a = 0.465808 + 0.565250I
b = 1.254740 + 0.247917I
−7.95058 + 3.07874I −19.9096 − 5.4080I
u = −0.669262 − 0.404635I
a = 0.465808 − 0.565250I
b = 1.254740 − 0.247917I
−7.95058 − 3.07874I −19.9096 + 5.4080I
u = 0.597312 + 0.499582I
a = −1.048900 + 0.571843I
b = 0.401917 − 0.758054I
2.07881 − 2.99552I −9.38208 + 5.15386I
u = 0.597312 − 0.499582I
a = −1.048900 − 0.571843I
b = 0.401917 + 0.758054I
2.07881 + 2.99552I −9.38208 − 5.15386I
u = 0.670676 + 0.356136I
a = 0.63994 − 3.06673I
b = 1.042790 + 0.370481I
−8.27974 − 2.07809I −20.0885 + 6.6662I
u = 0.670676 − 0.356136I
a = 0.63994 + 3.06673I
b = 1.042790 − 0.370481I
−8.27974 + 2.07809I −20.0885 − 6.6662I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.464343 + 0.536069I
a = 0.09506 − 1.92402I
b = −0.761545 + 0.651812I
−0.22536 + 4.12491I −12.4469 − 7.3915I
u = −0.464343 − 0.536069I
a = 0.09506 + 1.92402I
b = −0.761545 − 0.651812I
−0.22536 − 4.12491I −12.4469 + 7.3915I
u = −0.154574 + 0.651894I
a = 0.81766 + 1.18825I
b = −1.116310 − 0.581761I
−3.80714 − 7.87957I −14.4786 + 4.9899I
u = −0.154574 − 0.651894I
a = 0.81766 − 1.18825I
b = −1.116310 + 0.581761I
−3.80714 + 7.87957I −14.4786 − 4.9899I
u = 0.614548 + 0.255524I
a = −0.757214 + 0.499889I
b = −1.130020 + 0.157751I
−2.78857 − 0.70974I −15.3214 + 8.6751I
u = 0.614548 − 0.255524I
a = −0.757214 − 0.499889I
b = −1.130020 − 0.157751I
−2.78857 + 0.70974I −15.3214 − 8.6751I
u = −0.432857 + 0.495289I
a = 1.20679 + 0.74677I
b = −0.640326 − 0.609624I
−0.159008 − 0.526549I −12.09743 − 0.07898I
u = −0.432857 − 0.495289I
a = 1.20679 − 0.74677I
b = −0.640326 + 0.609624I
−0.159008 + 0.526549I −12.09743 + 0.07898I
u = 0.207458 + 0.606070I
a = −0.95467 + 1.17138I
b = 1.020010 − 0.576008I
1.44186 + 4.25219I −9.65797 − 4.16216I
u = 0.207458 − 0.606070I
a = −0.95467 − 1.17138I
b = 1.020010 + 0.576008I
1.44186 − 4.25219I −9.65797 + 4.16216I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.330405 + 0.540726I
a = −0.21935 − 1.63303I
b = 0.543025 + 0.677815I
2.85712 − 0.60484I −6.72055 + 2.73837I
u = 0.330405 − 0.540726I
a = −0.21935 + 1.63303I
b = 0.543025 − 0.677815I
2.85712 + 0.60484I −6.72055 − 2.73837I
u = −0.219371 + 0.590317I
a = 0.13232 − 1.46550I
b = −0.364491 + 0.774875I
−1.59296 − 2.77751I −11.43809 + 0.51083I
u = −0.219371 − 0.590317I
a = 0.13232 + 1.46550I
b = −0.364491 − 0.774875I
−1.59296 + 2.77751I −11.43809 − 0.51083I
u = −1.43199 + 0.05905I
a = 0.137202 + 0.892850I
b = 0.769513 − 0.690097I
−2.64448 + 2.59240I 0
u = −1.43199 − 0.05905I
a = 0.137202 − 0.892850I
b = 0.769513 + 0.690097I
−2.64448 − 2.59240I 0
u = −0.298512 + 0.480016I
a = 1.31900 + 1.05008I
b = −0.816807 − 0.489111I
−0.322274 − 0.536528I −12.40737 − 1.35367I
u = −0.298512 − 0.480016I
a = 1.31900 − 1.05008I
b = −0.816807 + 0.489111I
−0.322274 + 0.536528I −12.40737 + 1.35367I
u = 1.44062 + 0.04719I
a = 0.166631 − 0.612110I
b = −0.646775 + 0.712591I
−5.88879 − 1.18432I 0
u = 1.44062 − 0.04719I
a = 0.166631 + 0.612110I
b = −0.646775 − 0.712591I
−5.88879 + 1.18432I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47803 + 0.12168I
a = −0.385579 + 1.121210I
b = −0.883821 − 0.684109I
−6.54042 − 6.43614I 0
u = 1.47803 − 0.12168I
a = −0.385579 − 1.121210I
b = −0.883821 + 0.684109I
−6.54042 + 6.43614I 0
u = 1.52990
a = 1.17737
b = 1.28361
−12.4085 0
u = 1.54276 + 0.09438I
a = 0.536674 − 0.392892I
b = −0.398329 + 0.709261I
−6.76870 − 1.23124I 0
u = 1.54276 − 0.09438I
a = 0.536674 + 0.392892I
b = −0.398329 − 0.709261I
−6.76870 + 1.23124I 0
u = −1.56930 + 0.13818I
a = −0.509105 − 0.235933I
b = 0.316957 + 0.850275I
−5.21517 + 5.29137I 0
u = −1.56930 − 0.13818I
a = −0.509105 + 0.235933I
b = 0.316957 − 0.850275I
−5.21517 − 5.29137I 0
u = −1.58519 + 0.08012I
a = −1.075000 − 0.153161I
b = −1.247880 − 0.216923I
−10.34390 + 1.99279I 0
u = −1.58519 − 0.08012I
a = −1.075000 + 0.153161I
b = −1.247880 + 0.216923I
−10.34390 − 1.99279I 0
u = 1.58354 + 0.13428I
a = −0.90062 + 1.56369I
b = −1.091900 − 0.562937I
−8.80863 − 6.10945I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58354 − 0.13428I
a = −0.90062 − 1.56369I
b = −1.091900 + 0.562937I
−8.80863 + 6.10945I 0
u = −1.59498 + 0.02541I
a = −1.026250 − 0.269553I
b = 0.227957 + 0.286684I
−13.76460 + 0.04291I 0
u = −1.59498 − 0.02541I
a = −1.026250 + 0.269553I
b = 0.227957 − 0.286684I
−13.76460 − 0.04291I 0
u = −1.59687 + 0.10259I
a = 0.95169 + 1.95273I
b = 1.080760 − 0.462527I
−16.0269 + 3.7857I 0
u = −1.59687 − 0.10259I
a = 0.95169 − 1.95273I
b = 1.080760 + 0.462527I
−16.0269 − 3.7857I 0
u = 1.59634 + 0.11517I
a = 1.058470 − 0.213570I
b = 1.306430 − 0.292171I
−15.6716 − 5.0007I 0
u = 1.59634 − 0.11517I
a = 1.058470 + 0.213570I
b = 1.306430 + 0.292171I
−15.6716 + 5.0007I 0
u = 1.59603 + 0.15088I
a = 0.526312 − 0.168658I
b = −0.243882 + 0.912614I
−10.61980 − 9.02169I 0
u = 1.59603 − 0.15088I
a = 0.526312 + 0.168658I
b = −0.243882 − 0.912614I
−10.61980 + 9.02169I 0
u = −1.60049 + 0.15455I
a = 1.05682 + 1.42543I
b = 1.156870 − 0.592655I
−7.71958 + 10.61700I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60049 − 0.15455I
a = 1.05682 − 1.42543I
b = 1.156870 + 0.592655I
−7.71958 − 10.61700I 0
u = −0.131293 + 0.355319I
a = 0.20840 + 2.27516I
b = 1.145400 − 0.148687I
−6.48927 − 0.23669I −15.5734 − 1.1399I
u = −0.131293 − 0.355319I
a = 0.20840 − 2.27516I
b = 1.145400 + 0.148687I
−6.48927 + 0.23669I −15.5734 + 1.1399I
u = 1.61800 + 0.15854I
a = −1.17742 + 1.38527I
b = −1.204960 − 0.585327I
−13.5182 − 14.4723I 0
u = 1.61800 − 0.15854I
a = −1.17742 − 1.38527I
b = −1.204960 + 0.585327I
−13.5182 + 14.4723I 0
u = 1.63839 + 0.04440I
a = 0.969701 − 0.100633I
b = 1.021090 − 0.277570I
−10.84760 + 0.79068I 0
u = 1.63839 − 0.04440I
a = 0.969701 + 0.100633I
b = 1.021090 + 0.277570I
−10.84760 − 0.79068I 0
u = −1.64717
a = −0.905015
b = −0.467479
−13.9145 0
u = −0.339972
a = 0.935322
b = −0.240550
−0.545345 −17.9680
u = −1.66353 + 0.06990I
a = −0.938576 − 0.156768I
b = −1.076900 − 0.435530I
−16.2206 − 3.2650I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.66353 − 0.06990I
a = −0.938576 + 0.156768I
b = −1.076900 + 0.435530I
−16.2206 + 3.2650I 0
u = 0.311962
a = −5.58565
b = 0.860089
−6.70110 −11.7920
12
II. I
u
2
= hb − 1, a
2
− 2a + 2u − 3, u
2
− u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u + 1
a
12
=
−u
−u − 1
a
3
=
a
1
a
8
=
−u
−u
a
2
=
a + 1
1
a
1
=
1
0
a
5
=
−a
−1
a
9
=
au − 2
au − 2u
a
10
=
u
u
a
4
=
au − u − 1
au + a − u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
6
, c
7
(u
2
− u − 1)
2
c
10
, c
11
, c
12
(u
2
+ u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
8
c
9
(y −2)
4
c
6
, c
7
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −1.28825
b = 1.00000
−7.56670 −24.0000
u = −0.618034
a = 3.28825
b = 1.00000
−7.56670 −24.0000
u = 1.61803
a = 0.125968
b = 1.00000
−15.4624 −24.0000
u = 1.61803
a = 1.87403
b = 1.00000
−15.4624 −24.0000
16
III. I
u
3
= hb + 1, a + 1, u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u + 1
a
12
=
−u
−u + 1
a
3
=
−1
−1
a
8
=
u
u
a
2
=
−2
−1
a
1
=
−1
0
a
5
=
−1
−1
a
9
=
u
u
a
10
=
u
u
a
4
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
8
c
9
u
2
c
5
(u + 1)
2
c
6
, c
7
, c
10
u
2
+ u − 1
c
11
, c
12
u
2
− u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
2
c
3
, c
4
, c
8
c
9
y
2
c
6
, c
7
, c
10
c
11
, c
12
y
2
− 3y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.00000
b = −1.00000
−2.63189 −14.0000
u = −1.61803
a = −1.00000
b = −1.00000
−10.5276 −14.0000
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
72
+ 37u
71
+ ··· + 29u + 1)
c
2
((u − 1)
2
)(u + 1)
4
(u
72
+ 3u
71
+ ··· + 7u + 1)
c
3
, c
4
, c
9
u
2
(u
2
− 2)
2
(u
72
− u
71
+ ··· − 12u − 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
72
+ 3u
71
+ ··· + 7u + 1)
c
6
, c
7
((u
2
− u − 1)
2
)(u
2
+ u − 1)(u
72
− 2u
71
+ ··· + 2u + 1)
c
8
u
2
(u
2
− 2)
2
(u
72
+ 3u
71
+ ··· + 1492u + 220)
c
10
((u
2
+ u − 1)
3
)(u
72
− 20u
71
+ ··· − 348u + 113)
c
11
, c
12
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
72
− 2u
71
+ ··· + 2u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
72
+ 3y
71
+ ··· − 197y + 1)
c
2
, c
5
((y −1)
6
)(y
72
− 37y
71
+ ··· − 29y + 1)
c
3
, c
4
, c
9
y
2
(y −2)
4
(y
72
− 67y
71
+ ··· − 16y + 16)
c
6
, c
7
, c
11
c
12
((y
2
− 3y + 1)
3
)(y
72
− 84y
71
+ ··· − 20y + 1)
c
8
y
2
(y −2)
4
(y
72
− 7y
71
+ ··· − 402704y + 48400)
c
10
((y
2
− 3y + 1)
3
)(y
72
− 12y
71
+ ··· − 272524y + 12769)
22
