12a
0442
(K12a
0442
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 2 11 12 5 4 1 7 8
Solving Sequence
6,11
7 12
3,8
2 1 5 9 4 10
c
6
c
11
c
7
c
2
c
1
c
5
c
8
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.34896 × 10
18
u
56
+ 2.07087 × 10
18
u
55
+ ··· + 5.37832 × 10
18
b + 3.89959 × 10
18
,
1.80814 × 10
19
u
56
− 2.72100 × 10
19
u
55
+ ··· + 3.22699 × 10
19
a − 1.14340 × 10
20
, u
57
− 2u
56
+ ··· + 3u + 3i
I
u
2
= hb + 1, a + 1, u
2
+ u − 1i
I
u
3
= hb − 1, a
2
− 2a − 2u + 5, u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 63 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−1.35×10
18
u
56
+2.07×10
18
u
55
+· · ·+5.38×10
18
b+3.90×10
18
, 1.81×
10
19
u
56
−2.72×10
19
u
55
+· · ·+3.23×10
19
a−1.14×10
20
, u
57
−2u
56
+· · ·+3u+3i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
−0.560318u
56
+ 0.843200u
55
+ ··· + 3.40907u + 3.54324
0.250815u
56
− 0.385040u
55
+ ··· − 0.856790u − 0.725058
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−0.309503u
56
+ 0.458160u
55
+ ··· + 2.55228u + 2.81818
0.250815u
56
− 0.385040u
55
+ ··· − 0.856790u − 0.725058
a
1
=
u
3
− 2u
u
5
− 3u
3
+ u
a
5
=
0.171913u
56
− 0.402348u
55
+ ··· − 5.30776u − 1.55172
−0.0224250u
56
+ 0.0733178u
55
+ ··· + 1.08954u − 0.313317
a
9
=
−1.20094u
56
+ 0.0915331u
55
+ ··· + 12.1379u + 5.33793
−0.604807u
56
− 0.136946u
55
+ ··· − 0.482139u + 1.18193
a
4
=
−0.837757u
56
+ 1.11941u
55
+ ··· + 4.97460u + 4.32404
0.144564u
56
− 0.142864u
55
+ ··· + 0.629938u − 0.344274
a
10
=
u
7
− 4u
5
+ 4u
3
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
826313162299306861
5378323049132608541
u
56
−
1448839852347394239
5378323049132608541
u
55
+ ··· +
11912765712166984528
5378323049132608541
u −
107418126212947908801
5378323049132608541
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
57
+ 27u
56
+ ··· + 3644u + 121
c
2
, c
5
u
57
+ 3u
56
+ ··· + 50u + 11
c
3
, c
4
, c
8
c
9
u
57
+ u
56
+ ··· + 16u + 4
c
6
, c
7
, c
11
c
12
u
57
− 2u
56
+ ··· + 3u + 3
c
10
u
57
− 14u
56
+ ··· − 681u + 369
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
57
+ 13y
56
+ ··· + 4124360y −14641
c
2
, c
5
y
57
− 27y
56
+ ··· + 3644y −121
c
3
, c
4
, c
8
c
9
y
57
+ 67y
56
+ ··· − 64y −16
c
6
, c
7
, c
11
c
12
y
57
− 66y
56
+ ··· + 183y −9
c
10
y
57
+ 6y
56
+ ··· + 3023883y −136161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704131 + 0.589103I
a = −0.55492 − 1.95508I
b = −1.137580 + 0.679596I
8.22701 + 10.27850I −9.75435 − 7.77331I
u = −0.704131 − 0.589103I
a = −0.55492 + 1.95508I
b = −1.137580 − 0.679596I
8.22701 − 10.27850I −9.75435 + 7.77331I
u = 1.076280 + 0.226599I
a = −0.275618 − 0.007670I
b = −0.916195 + 0.661079I
5.36877 + 2.70273I 0
u = 1.076280 − 0.226599I
a = −0.275618 + 0.007670I
b = −0.916195 − 0.661079I
5.36877 − 2.70273I 0
u = −0.864189 + 0.160463I
a = 0.551285 + 0.098003I
b = 0.901677 + 0.376998I
−2.19905 − 1.48805I −14.3910 + 4.5059I
u = −0.864189 − 0.160463I
a = 0.551285 − 0.098003I
b = 0.901677 − 0.376998I
−2.19905 + 1.48805I −14.3910 − 4.5059I
u = −0.616683 + 0.599939I
a = 0.971008 + 0.626841I
b = −0.464660 − 0.924311I
10.27110 + 4.39988I −6.95656 − 3.67714I
u = −0.616683 − 0.599939I
a = 0.971008 − 0.626841I
b = −0.464660 + 0.924311I
10.27110 − 4.39988I −6.95656 + 3.67714I
u = 0.663557 + 0.528050I
a = 0.46790 − 2.15581I
b = 1.061910 + 0.603362I
0.29697 − 7.63210I −12.1110 + 9.6571I
u = 0.663557 − 0.528050I
a = 0.46790 + 2.15581I
b = 1.061910 − 0.603362I
0.29697 + 7.63210I −12.1110 − 9.6571I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595377 + 0.457995I
a = −0.17328 − 2.41340I
b = −0.951412 + 0.515712I
−1.24820 + 3.57057I −14.6209 − 5.6248I
u = −0.595377 − 0.457995I
a = −0.17328 + 2.41340I
b = −0.951412 − 0.515712I
−1.24820 − 3.57057I −14.6209 + 5.6248I
u = −0.342193 + 0.661292I
a = 0.03195 − 1.59816I
b = −0.580638 + 0.877264I
11.08210 − 0.14823I −5.35375 − 2.36234I
u = −0.342193 − 0.661292I
a = 0.03195 + 1.59816I
b = −0.580638 − 0.877264I
11.08210 + 0.14823I −5.35375 + 2.36234I
u = 0.554979 + 0.489624I
a = −1.094900 + 0.593600I
b = 0.455941 − 0.705482I
2.03839 − 2.59914I −8.23652 + 5.38103I
u = 0.554979 − 0.489624I
a = −1.094900 − 0.593600I
b = 0.455941 + 0.705482I
2.03839 + 2.59914I −8.23652 − 5.38103I
u = −0.235908 + 0.693140I
a = 0.858831 + 1.042160I
b = −1.063010 − 0.700463I
9.61427 − 5.97551I −6.95096 + 2.88432I
u = −0.235908 − 0.693140I
a = 0.858831 − 1.042160I
b = −1.063010 + 0.700463I
9.61427 + 5.97551I −6.95096 − 2.88432I
u = −0.496534 + 0.436861I
a = 0.496412 + 0.893237I
b = 1.299830 + 0.083523I
3.92009 + 1.55212I −10.02210 − 4.28622I
u = −0.496534 − 0.436861I
a = 0.496412 − 0.893237I
b = 1.299830 − 0.083523I
3.92009 − 1.55212I −10.02210 + 4.28622I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.335210 + 0.150895I
a = −0.452216 + 0.700456I
b = −0.764404 − 0.811299I
5.80019 − 2.81830I 0
u = 1.335210 − 0.150895I
a = −0.452216 − 0.700456I
b = −0.764404 + 0.811299I
5.80019 + 2.81830I 0
u = 0.603584 + 0.236433I
a = −0.804681 + 0.489871I
b = −1.119030 + 0.142393I
−2.75711 − 0.66564I −14.7826 + 9.4775I
u = 0.603584 − 0.236433I
a = −0.804681 − 0.489871I
b = −1.119030 − 0.142393I
−2.75711 + 0.66564I −14.7826 − 9.4775I
u = 0.239924 + 0.586288I
a = −1.02557 + 1.13352I
b = 0.966676 − 0.579065I
1.52522 + 3.82244I −8.59714 − 4.32635I
u = 0.239924 − 0.586288I
a = −1.02557 − 1.13352I
b = 0.966676 + 0.579065I
1.52522 − 3.82244I −8.59714 + 4.32635I
u = 0.363750 + 0.490876I
a = −0.32703 − 1.72685I
b = 0.591846 + 0.590762I
2.57252 − 0.84095I −6.12773 + 3.38170I
u = 0.363750 − 0.490876I
a = −0.32703 + 1.72685I
b = 0.591846 − 0.590762I
2.57252 + 0.84095I −6.12773 − 3.38170I
u = 0.468640 + 0.278951I
a = −1.53706 − 2.70780I
b = 0.779461 + 0.243702I
3.07197 − 1.00767I −8.24371 + 7.05136I
u = 0.468640 − 0.278951I
a = −1.53706 + 2.70780I
b = 0.779461 − 0.243702I
3.07197 + 1.00767I −8.24371 − 7.05136I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46667 + 0.00945I
a = −0.143513 + 0.884230I
b = 0.701842 − 0.637996I
−3.17986 + 2.29539I 0
u = −1.46667 − 0.00945I
a = −0.143513 − 0.884230I
b = 0.701842 + 0.637996I
−3.17986 − 2.29539I 0
u = −0.320993 + 0.413524I
a = 1.53117 + 0.94240I
b = −0.744681 − 0.411258I
−0.459717 − 0.404026I −12.49447 − 1.15280I
u = −0.320993 − 0.413524I
a = 1.53117 − 0.94240I
b = −0.744681 + 0.411258I
−0.459717 + 0.404026I −12.49447 + 1.15280I
u = 1.52983 + 0.07395I
a = 0.533941 − 0.495207I
b = −0.455361 + 0.657851I
−6.82775 − 0.90726I 0
u = 1.52983 − 0.07395I
a = 0.533941 + 0.495207I
b = −0.455361 − 0.657851I
−6.82775 + 0.90726I 0
u = −1.53547 + 0.08531I
a = 0.24044 + 1.57007I
b = 0.906529 − 0.539225I
−3.70478 + 2.30339I 0
u = −1.53547 − 0.08531I
a = 0.24044 − 1.57007I
b = 0.906529 + 0.539225I
−3.70478 − 2.30339I 0
u = 1.54418 + 0.11457I
a = 1.146410 − 0.213923I
b = 1.364410 − 0.193878I
−2.97244 − 3.47012I 0
u = 1.54418 − 0.11457I
a = 1.146410 + 0.213923I
b = 1.364410 + 0.193878I
−2.97244 + 3.47012I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55226 + 0.13383I
a = −0.483951 − 0.274353I
b = 0.366394 + 0.829437I
−5.02892 + 4.81975I 0
u = −1.55226 − 0.13383I
a = −0.483951 + 0.274353I
b = 0.366394 − 0.829437I
−5.02892 − 4.81975I 0
u = 1.56988 + 0.13059I
a = −0.77974 + 1.54885I
b = −1.055050 − 0.572617I
−8.56290 − 5.70715I 0
u = 1.56988 − 0.13059I
a = −0.77974 − 1.54885I
b = −1.055050 + 0.572617I
−8.56290 + 5.70715I 0
u = 1.56630 + 0.18220I
a = 0.438140 − 0.169691I
b = −0.359969 + 0.971927I
2.99794 − 7.27238I 0
u = 1.56630 − 0.18220I
a = 0.438140 + 0.169691I
b = −0.359969 − 0.971927I
2.99794 + 7.27238I 0
u = −1.58131 + 0.07034I
a = −1.081170 − 0.135333I
b = −1.236560 − 0.191168I
−10.26270 + 1.82090I 0
u = −1.58131 − 0.07034I
a = −1.081170 + 0.135333I
b = −1.236560 + 0.191168I
−10.26270 − 1.82090I 0
u = −1.58968 + 0.15765I
a = 0.98367 + 1.39881I
b = 1.133960 − 0.611529I
−7.29789 + 10.17520I 0
u = −1.58968 − 0.15765I
a = 0.98367 − 1.39881I
b = 1.133960 + 0.611529I
−7.29789 − 10.17520I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60528 + 0.18171I
a = −1.07959 + 1.25671I
b = −1.194090 − 0.654261I
0.45530 − 13.17410I 0
u = 1.60528 − 0.18171I
a = −1.07959 − 1.25671I
b = −1.194090 + 0.654261I
0.45530 + 13.17410I 0
u = 1.63713 + 0.03909I
a = 0.969700 − 0.089889I
b = 1.003290 − 0.255169I
−10.78670 + 0.74355I 0
u = 1.63713 − 0.03909I
a = 0.969700 + 0.089889I
b = 1.003290 + 0.255169I
−10.78670 − 0.74355I 0
u = −0.355161
a = 0.961312
b = −0.240286
−0.558297 −17.5620
u = −1.67953 + 0.03241I
a = −0.888295 − 0.107233I
b = −0.870985 − 0.473795I
−4.14213 − 1.93573I 0
u = −1.67953 − 0.03241I
a = −0.888295 + 0.107233I
b = −0.870985 + 0.473795I
−4.14213 + 1.93573I 0
10
II. I
u
2
= 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
4
=
−1
−1
a
10
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14
11
(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
12
(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
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−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
14
III. I
u
3
= hb − 1, a
2
− 2a − 2u + 5, 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 − 4u + 2
au − 2u
a
4
=
au + 2a − u − 1
au + a − u
a
10
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
15
(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
16
(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
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.00000 + 2.28825I
b = 1.00000
2.30291 −16.0000
u = −0.618034
a = 1.00000 − 2.28825I
b = 1.00000
2.30291 −16.0000
u = 1.61803
a = 1.000000 + 0.874032I
b = 1.00000
−5.59278 −16.0000
u = 1.61803
a = 1.000000 − 0.874032I
b = 1.00000
−5.59278 −16.0000
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
57
+ 27u
56
+ ··· + 3644u + 121)
c
2
((u − 1)
2
)(u + 1)
4
(u
57
+ 3u
56
+ ··· + 50u + 11)
c
3
, c
4
, c
8
c
9
u
2
(u
2
+ 2)
2
(u
57
+ u
56
+ ··· + 16u + 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
57
+ 3u
56
+ ··· + 50u + 11)
c
6
, c
7
((u
2
− u − 1)
2
)(u
2
+ u − 1)(u
57
− 2u
56
+ ··· + 3u + 3)
c
10
((u
2
+ u − 1)
3
)(u
57
− 14u
56
+ ··· − 681u + 369)
c
11
, c
12
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
57
− 2u
56
+ ··· + 3u + 3)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
57
+ 13y
56
+ ··· + 4124360y −14641)
c
2
, c
5
((y −1)
6
)(y
57
− 27y
56
+ ··· + 3644y −121)
c
3
, c
4
, c
8
c
9
y
2
(y + 2)
4
(y
57
+ 67y
56
+ ··· − 64y −16)
c
6
, c
7
, c
11
c
12
((y
2
− 3y + 1)
3
)(y
57
− 66y
56
+ ··· + 183y −9)
c
10
((y
2
− 3y + 1)
3
)(y
57
+ 6y
56
+ ··· + 3023883y −136161)
20
