12a
0848
(K12a
0848
)
A knot diagram
1
Linearized knot diagam
4 5 9 8 3 11 12 2 1 6 7 10
Solving Sequence
6,11
7 12
3,8
5 2 4 10 1 9
c
6
c
11
c
7
c
5
c
2
c
4
c
10
c
12
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h6.79509 × 10
25
u
81
− 1.87697 × 10
26
u
80
+ ··· + 3.12829 × 10
26
b + 3.70010 × 10
26
,
− 1.25500 × 10
27
u
81
+ 4.42966 × 10
27
u
80
+ ··· + 3.12829 × 10
26
a − 3.60905 × 10
27
, u
82
− 2u
81
+ ··· + 5u + 1i
I
u
2
= hb − 1, a − u + 4, u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 84 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
= h6.80×10
25
u
81
−1.88×10
26
u
80
+· · ·+3.13×10
26
b+3.70×10
26
, −1.26×
10
27
u
81
+4.43×10
27
u
80
+· · ·+3.13×10
26
a−3.61×10
27
, u
82
−2u
81
+· · ·+5u+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
=
4.01178u
81
− 14.1600u
80
+ ··· + 49.3240u + 11.5368
−0.217214u
81
+ 0.599999u
80
+ ··· − 0.525322u − 1.18279
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−3.73565u
81
+ 13.7600u
80
+ ··· − 50.1788u − 10.6699
0.131143u
81
− 0.600003u
80
+ ··· + 0.898711u + 1.26886
a
2
=
1.23051u
81
− 0.600008u
80
+ ··· − 4.81570u + 0.0834147
−0.827859u
81
+ 7.27353 × 10
−6
u
80
+ ··· + 4.25322u + 0.827859
a
4
=
−3.69924u
81
+ 10.1600u
80
+ ··· − 30.3291u − 6.30999
0.0984670u
81
+ 1.40003u
80
+ ··· − 9.34157u − 1.49847
a
10
=
−u
u
a
1
=
−u
5
+ 2u
3
+ u
u
5
− 3u
3
+ u
a
9
=
−u
9
+ 4u
7
− 3u
5
− 2u
3
− u
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
12431619809245966583934679162
312829021899527050766390809
u
81
+
35624969286962567890354505997
312829021899527050766390809
u
80
+ ··· −
83891237795955352645480927062
312829021899527050766390809
u −
25270533899815883781765835149
312829021899527050766390809
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
− 13u
81
+ ··· + 20u + 4
c
2
, c
5
u
82
+ 3u
81
+ ··· − 10u + 1
c
3
u
82
− 41u
80
+ ··· − 320u + 56
c
4
u
82
− 2u
81
+ ··· + 9u + 1
c
6
, c
7
, c
10
c
11
u
82
+ 2u
81
+ ··· − 5u + 1
c
8
u
82
+ 4u
81
+ ··· + u + 1
c
9
, c
12
u
82
+ 14u
81
+ ··· + 13953u + 1583
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
− 15y
81
+ ··· − 424y + 16
c
2
, c
5
y
82
− 49y
81
+ ··· − 138y + 1
c
3
y
82
− 82y
81
+ ··· − 254496y + 3136
c
4
y
82
− 78y
81
+ ··· − 291y + 1
c
6
, c
7
, c
10
c
11
y
82
− 90y
81
+ ··· − 3y + 1
c
8
y
82
+ 10y
81
+ ··· − 3y + 1
c
9
, c
12
y
82
+ 54y
81
+ ··· + 132694021y + 2505889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.870995
a = −1.72046
b = 0.696147
1.59278 0
u = 0.811511 + 0.271221I
a = −2.19736 + 0.75030I
b = 1.239060 + 0.452098I
4.42119 + 8.06572I 0
u = 0.811511 − 0.271221I
a = −2.19736 − 0.75030I
b = 1.239060 − 0.452098I
4.42119 − 8.06572I 0
u = −0.594864 + 0.611462I
a = −1.22801 − 2.05470I
b = 1.31195 − 0.61880I
−1.30842 − 13.62090I 0
u = −0.594864 − 0.611462I
a = −1.22801 + 2.05470I
b = 1.31195 + 0.61880I
−1.30842 + 13.62090I 0
u = −0.764155 + 0.376279I
a = −1.13837 − 1.23153I
b = 1.113830 + 0.304908I
3.83447 + 1.89000I 0
u = −0.764155 − 0.376279I
a = −1.13837 + 1.23153I
b = 1.113830 − 0.304908I
3.83447 − 1.89000I 0
u = 0.610557 + 0.592676I
a = −1.25430 + 1.40948I
b = 0.964576 + 0.401078I
−2.62652 + 5.81470I 0
u = 0.610557 − 0.592676I
a = −1.25430 − 1.40948I
b = 0.964576 − 0.401078I
−2.62652 − 5.81470I 0
u = −0.556885 + 0.597439I
a = 1.214540 + 0.434604I
b = 0.184378 + 1.180630I
−4.87343 − 7.34073I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556885 − 0.597439I
a = 1.214540 − 0.434604I
b = 0.184378 − 1.180630I
−4.87343 + 7.34073I 0
u = 0.528286 + 0.620135I
a = 0.124296 + 0.097755I
b = 0.406875 − 0.376887I
−4.10622 + 2.32469I 0
u = 0.528286 − 0.620135I
a = 0.124296 − 0.097755I
b = 0.406875 + 0.376887I
−4.10622 − 2.32469I 0
u = 0.462275 + 0.639883I
a = −0.332685 + 0.621312I
b = 0.536469 + 0.377022I
−4.30287 + 1.94000I 0
u = 0.462275 − 0.639883I
a = −0.332685 − 0.621312I
b = 0.536469 − 0.377022I
−4.30287 − 1.94000I 0
u = −0.543646 + 0.553436I
a = 0.95361 + 2.22060I
b = −1.18611 + 0.80921I
0.40590 − 5.34297I 6.00000 + 9.52274I
u = −0.543646 − 0.553436I
a = 0.95361 − 2.22060I
b = −1.18611 − 0.80921I
0.40590 + 5.34297I 6.00000 − 9.52274I
u = 0.513004 + 0.563882I
a = 0.90964 − 3.31132I
b = −0.978158 − 0.173023I
−1.20160 + 2.58017I 6.00000 + 7.53733I
u = 0.513004 − 0.563882I
a = 0.90964 + 3.31132I
b = −0.978158 + 0.173023I
−1.20160 − 2.58017I 6.00000 − 7.53733I
u = −0.384471 + 0.651387I
a = 0.161962 + 0.374695I
b = 1.28132 + 0.61475I
−1.93003 + 9.35126I 6.00000 − 4.19971I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.384471 − 0.651387I
a = 0.161962 − 0.374695I
b = 1.28132 − 0.61475I
−1.93003 − 9.35126I 6.00000 + 4.19971I
u = −0.423577 + 0.616541I
a = −0.612466 − 1.070720I
b = 0.227379 − 1.135570I
−5.26621 + 3.21097I 2.08818 − 1.93788I
u = −0.423577 − 0.616541I
a = −0.612466 + 1.070720I
b = 0.227379 + 1.135570I
−5.26621 − 3.21097I 2.08818 + 1.93788I
u = 0.469113 + 0.564443I
a = −0.00398 + 1.58925I
b = −0.924415 + 0.181797I
−1.33155 + 1.29922I 5.09604 − 13.12638I
u = 0.469113 − 0.564443I
a = −0.00398 − 1.58925I
b = −0.924415 − 0.181797I
−1.33155 − 1.29922I 5.09604 + 13.12638I
u = 0.354693 + 0.630587I
a = −0.277083 − 0.223148I
b = 0.879813 − 0.422336I
−3.37714 − 1.66121I 1.62414 + 2.54415I
u = 0.354693 − 0.630587I
a = −0.277083 + 0.223148I
b = 0.879813 + 0.422336I
−3.37714 + 1.66121I 1.62414 − 2.54415I
u = −0.501466 + 0.511705I
a = 0.13756 + 1.63725I
b = −1.55579 − 0.07559I
1.77607 − 1.77523I 11.62947 + 4.03448I
u = −0.501466 − 0.511705I
a = 0.13756 − 1.63725I
b = −1.55579 + 0.07559I
1.77607 + 1.77523I 11.62947 − 4.03448I
u = −0.427166 + 0.550491I
a = −0.978268 − 0.385975I
b = −1.083790 − 0.789192I
0.06386 + 1.53089I 8.01853 − 2.55528I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.427166 − 0.550491I
a = −0.978268 + 0.385975I
b = −1.083790 + 0.789192I
0.06386 − 1.53089I 8.01853 + 2.55528I
u = 0.638658 + 0.225748I
a = 0.389590 + 0.593475I
b = −0.065745 − 0.839937I
0.57980 + 3.50184I 9.13977 − 8.90490I
u = 0.638658 − 0.225748I
a = 0.389590 − 0.593475I
b = −0.065745 + 0.839937I
0.57980 − 3.50184I 9.13977 + 8.90490I
u = 0.652505 + 0.065512I
a = 2.65287 − 0.29373I
b = −1.316620 − 0.452019I
4.30182 + 1.62654I 18.7241 − 4.7341I
u = 0.652505 − 0.065512I
a = 2.65287 + 0.29373I
b = −1.316620 + 0.452019I
4.30182 − 1.62654I 18.7241 + 4.7341I
u = −0.053845 + 0.582038I
a = −0.014038 − 0.437876I
b = 1.139860 − 0.413488I
1.64921 − 5.15659I 5.38071 + 6.28870I
u = −0.053845 − 0.582038I
a = −0.014038 + 0.437876I
b = 1.139860 + 0.413488I
1.64921 + 5.15659I 5.38071 − 6.28870I
u = −1.42911 + 0.12607I
a = −1.021550 − 0.129914I
b = 0.738343 + 0.519400I
2.22829 − 0.95699I 0
u = −1.42911 − 0.12607I
a = −1.021550 + 0.129914I
b = 0.738343 − 0.519400I
2.22829 + 0.95699I 0
u = 1.42513 + 0.16645I
a = −0.951642 + 0.179384I
b = 1.230580 − 0.607759I
3.83137 − 6.45058I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42513 − 0.16645I
a = −0.951642 − 0.179384I
b = 1.230580 + 0.607759I
3.83137 + 6.45058I 0
u = −0.545660 + 0.113928I
a = −0.983595 + 0.442700I
b = −0.1046930 − 0.0437336I
0.978391 − 0.167632I 10.95193 + 1.32595I
u = −0.545660 − 0.113928I
a = −0.983595 − 0.442700I
b = −0.1046930 + 0.0437336I
0.978391 + 0.167632I 10.95193 − 1.32595I
u = −0.529899
a = 10.3142
b = −1.02032
2.51211 −88.5500
u = 1.47193 + 0.16091I
a = −0.855076 + 0.061099I
b = 0.297685 + 1.084440I
0.865552 − 0.485531I 0
u = 1.47193 − 0.16091I
a = −0.855076 − 0.061099I
b = 0.297685 − 1.084440I
0.865552 + 0.485531I 0
u = −1.48145 + 0.19094I
a = −0.844562 − 0.272193I
b = 0.669605 − 0.422650I
2.01541 − 4.91638I 0
u = −1.48145 − 0.19094I
a = −0.844562 + 0.272193I
b = 0.669605 + 0.422650I
2.01541 + 4.91638I 0
u = 1.50668 + 0.13219I
a = −0.036896 − 0.447336I
b = −0.940587 + 0.842768I
6.42569 + 0.77348I 0
u = 1.50668 − 0.13219I
a = −0.036896 + 0.447336I
b = −0.940587 − 0.842768I
6.42569 − 0.77348I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51364 + 0.15219I
a = 0.536167 − 1.247610I
b = −0.866187 − 0.214071I
5.21063 − 3.80691I 0
u = −1.51364 − 0.15219I
a = 0.536167 + 1.247610I
b = −0.866187 + 0.214071I
5.21063 + 3.80691I 0
u = −1.53024 + 0.16174I
a = 2.19828 + 2.75110I
b = −1.021300 + 0.173147I
5.57532 − 5.16892I 0
u = −1.53024 − 0.16174I
a = 2.19828 − 2.75110I
b = −1.021300 − 0.173147I
5.57532 + 5.16892I 0
u = −1.52923 + 0.18520I
a = −0.206185 − 0.261817I
b = 0.296189 + 0.412108I
2.67887 − 5.22504I 0
u = −1.52923 − 0.18520I
a = −0.206185 + 0.261817I
b = 0.296189 − 0.412108I
2.67887 + 5.22504I 0
u = 1.54149 + 0.02620I
a = −0.413194 − 0.502741I
b = −0.273232 − 0.149623I
8.01688 + 0.66095I 0
u = 1.54149 − 0.02620I
a = −0.413194 + 0.502741I
b = −0.273232 + 0.149623I
8.01688 − 0.66095I 0
u = 1.53502 + 0.14471I
a = 1.76397 − 1.36906I
b = −1.62122 + 0.15951I
8.58492 + 4.10520I 0
u = 1.53502 − 0.14471I
a = 1.76397 + 1.36906I
b = −1.62122 − 0.15951I
8.58492 − 4.10520I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54999
a = 5.72235
b = −1.07156
9.62835 0
u = 1.54264 + 0.16225I
a = 1.98586 − 1.16029I
b = −1.25596 − 0.83173I
7.35240 + 7.92215I 0
u = 1.54264 − 0.16225I
a = 1.98586 + 1.16029I
b = −1.25596 + 0.83173I
7.35240 − 7.92215I 0
u = 1.54406 + 0.18057I
a = 0.898342 + 0.570588I
b = 0.148551 − 1.220200I
2.09607 + 10.16370I 0
u = 1.54406 − 0.18057I
a = 0.898342 − 0.570588I
b = 0.148551 + 1.220200I
2.09607 − 10.16370I 0
u = −1.56208 + 0.04407I
a = 0.356577 − 1.009890I
b = −0.205192 + 0.989853I
8.00277 − 4.37968I 0
u = −1.56208 − 0.04407I
a = 0.356577 + 1.009890I
b = −0.205192 − 0.989853I
8.00277 + 4.37968I 0
u = −1.56847 + 0.01217I
a = 2.90549 − 0.18562I
b = −1.44541 + 0.51761I
11.82620 − 1.87309I 0
u = −1.56847 − 0.01217I
a = 2.90549 + 0.18562I
b = −1.44541 − 0.51761I
11.82620 + 1.87309I 0
u = 1.55988 + 0.18904I
a = −2.19841 + 1.29679I
b = 1.33759 + 0.61959I
5.8572 + 16.5563I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55988 − 0.18904I
a = −2.19841 − 1.29679I
b = 1.33759 − 0.61959I
5.8572 − 16.5563I 0
u = −1.56748 + 0.18297I
a = −1.93274 − 0.91566I
b = 1.026650 − 0.384762I
4.64101 − 8.66957I 0
u = −1.56748 − 0.18297I
a = −1.93274 + 0.91566I
b = 1.026650 + 0.384762I
4.64101 + 8.66957I 0
u = 0.064511 + 0.412780I
a = −0.902893 + 0.694446I
b = 0.152912 + 0.585524I
−1.19387 − 1.28666I −0.50594 + 1.92491I
u = 0.064511 − 0.412780I
a = −0.902893 − 0.694446I
b = 0.152912 − 0.585524I
−1.19387 + 1.28666I −0.50594 − 1.92491I
u = −1.60578 + 0.05889I
a = −2.75309 − 0.20122I
b = 1.313760 − 0.435079I
12.6240 − 9.1945I 0
u = −1.60578 − 0.05889I
a = −2.75309 + 0.20122I
b = 1.313760 + 0.435079I
12.6240 + 9.1945I 0
u = 1.60958 + 0.08865I
a = −2.02010 + 0.86926I
b = 1.157150 − 0.210437I
11.93040 − 0.22921I 0
u = 1.60958 − 0.08865I
a = −2.02010 − 0.86926I
b = 1.157150 + 0.210437I
11.93040 + 0.22921I 0
u = 1.64214
a = −2.06417
b = 0.911522
10.2733 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.153931 + 0.229405I
a = −2.65823 + 0.79988I
b = −1.068010 + 0.189730I
1.95141 − 0.72099I 4.92941 − 0.08019I
u = −0.153931 − 0.229405I
a = −2.65823 − 0.79988I
b = −1.068010 − 0.189730I
1.95141 + 0.72099I 4.92941 + 0.08019I
13
II. I
u
2
= hb − 1, a − u + 4, 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
=
u − 4
1
a
8
=
−u
u
a
5
=
u − 3
1
a
2
=
−1
0
a
4
=
u − 2
0
a
10
=
−u
u
a
1
=
−1
0
a
9
=
−2u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 21
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
c
2
(u + 1)
2
c
3
, c
4
, c
6
c
7
, c
8
, c
9
u
2
− u − 1
c
5
(u − 1)
2
c
10
, c
11
, c
12
u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
c
2
, c
5
(y −1)
2
c
3
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
2
− 3y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −4.61803
b = 1.00000
2.63189 21.0000
u = 1.61803
a = −2.38197
b = 1.00000
10.5276 21.0000
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
82
− 13u
81
+ ··· + 20u + 4)
c
2
((u + 1)
2
)(u
82
+ 3u
81
+ ··· − 10u + 1)
c
3
(u
2
− u − 1)(u
82
− 41u
80
+ ··· − 320u + 56)
c
4
(u
2
− u − 1)(u
82
− 2u
81
+ ··· + 9u + 1)
c
5
((u − 1)
2
)(u
82
+ 3u
81
+ ··· − 10u + 1)
c
6
, c
7
(u
2
− u − 1)(u
82
+ 2u
81
+ ··· − 5u + 1)
c
8
(u
2
− u − 1)(u
82
+ 4u
81
+ ··· + u + 1)
c
9
(u
2
− u − 1)(u
82
+ 14u
81
+ ··· + 13953u + 1583)
c
10
, c
11
(u
2
+ u − 1)(u
82
+ 2u
81
+ ··· − 5u + 1)
c
12
(u
2
+ u − 1)(u
82
+ 14u
81
+ ··· + 13953u + 1583)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y
82
− 15y
81
+ ··· − 424y + 16)
c
2
, c
5
((y −1)
2
)(y
82
− 49y
81
+ ··· − 138y + 1)
c
3
(y
2
− 3y + 1)(y
82
− 82y
81
+ ··· − 254496y + 3136)
c
4
(y
2
− 3y + 1)(y
82
− 78y
81
+ ··· − 291y + 1)
c
6
, c
7
, c
10
c
11
(y
2
− 3y + 1)(y
82
− 90y
81
+ ··· − 3y + 1)
c
8
(y
2
− 3y + 1)(y
82
+ 10y
81
+ ··· − 3y + 1)
c
9
, c
12
(y
2
− 3y + 1)(y
82
+ 54y
81
+ ··· + 1.32694 × 10
8
y + 2505889)
19
