12a
1095
(K12a
1095
)
A knot diagram
1
Linearized knot diagam
4 7 10 1 12 9 3 11 2 8 6 5
Solving Sequence
1,5
4
2,9
10 3 12 6 7 11 8
c
4
c
1
c
9
c
3
c
12
c
5
c
6
c
11
c
8
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.34837 × 10
27
u
52
− 2.41782 × 10
27
u
51
+ ··· + 2.76539 × 10
27
b − 4.01656 × 10
27
,
− 3.41977 × 10
27
u
52
+ 6.63330 × 10
27
u
51
+ ··· + 5.53078 × 10
27
a + 3.25207 × 10
27
, u
53
− 2u
52
+ ··· − 3u + 1i
I
u
2
= hu
3
+ 2u
2
+ 4b + 5u + 3, −5u
3
− 2u
2
+ 8a − 9u − 3, u
4
+ u
3
+ 3u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 57 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
= h1.35×10
27
u
52
−2.42×10
27
u
51
+· · ·+2.77×10
27
b−4.02×10
27
, −3.42×
10
27
u
52
+6.63×10
27
u
51
+· · ·+5.53×10
27
a+3.25×10
27
, u
53
−2u
52
+· · ·−3u+1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
0.618315u
52
− 1.19934u
51
+ ··· + 8.80138u − 0.587995
−0.487586u
52
+ 0.874316u
51
+ ··· − 2.83559u + 1.45244
a
10
=
0.530284u
52
− 1.04842u
51
+ ··· + 8.32484u − 0.480894
−0.408912u
52
+ 0.748136u
51
+ ··· − 2.37166u + 1.32020
a
3
=
0.0838946u
52
− 0.639715u
51
+ ··· − 3.71956u − 0.610289
−0.0738827u
52
+ 0.330937u
51
+ ··· + 4.07454u − 0.785735
a
12
=
u
u
a
6
=
u
2
+ 1
u
2
a
7
=
−1.11189u
52
+ 2.28145u
51
+ ··· − 7.30635u − 0.400627
0.307946u
52
− 0.571956u
51
+ ··· + 6.37995u − 2.10022
a
11
=
u
3
+ 2u
u
3
+ u
a
8
=
0.780510u
52
− 1.54138u
51
+ ··· + 7.33530u − 1.15081
−0.419078u
52
+ 0.718479u
51
+ ··· − 3.61371u + 1.17045
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.212314u
52
+ 1.34571u
51
+ ··· + 2.23825u + 7.42547
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
11
, c
12
u
53
− 2u
52
+ ··· − 3u + 1
c
2
, c
7
u
53
+ 2u
52
+ ··· + 3u − 1
c
3
8(8u
53
− 11u
52
+ ··· + 480u + 3943)
c
6
8(8u
53
− 7u
52
+ ··· + 348462u + 61297)
c
8
, c
10
u
53
+ 5u
52
+ ··· − 17u − 64
c
9
u
53
− 3u
52
+ ··· − 576u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
, c
12
y
53
+ 72y
52
+ ··· − 13y −1
c
2
, c
7
y
53
− 36y
52
+ ··· − 13y −1
c
3
64(64y
53
+ 2007y
52
+ ··· − 9.98193 × 10
7
y −1.55472 × 10
7
)
c
6
64(64y
53
− 3105y
52
+ ··· + 2.44146 × 10
10
y −3.75732 × 10
9
)
c
8
, c
10
y
53
− 49y
52
+ ··· + 68129y −4096
c
9
y
53
+ 27y
52
+ ··· − 8925184y −1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097309 + 1.013130I
a = 1.06909 + 1.45901I
b = −0.293233 − 0.247581I
5.81488 + 0.01278I 0
u = 0.097309 − 1.013130I
a = 1.06909 − 1.45901I
b = −0.293233 + 0.247581I
5.81488 − 0.01278I 0
u = −0.170586 + 1.030690I
a = −0.621933 + 0.377743I
b = 0.745819 + 0.222778I
2.87981 + 2.52887I 0
u = −0.170586 − 1.030690I
a = −0.621933 − 0.377743I
b = 0.745819 − 0.222778I
2.87981 − 2.52887I 0
u = 0.043294 + 1.080920I
a = 0.98039 − 1.04863I
b = −0.415517 − 0.941732I
5.95677 − 1.10474I 0
u = 0.043294 − 1.080920I
a = 0.98039 + 1.04863I
b = −0.415517 + 0.941732I
5.95677 + 1.10474I 0
u = 0.183709 + 1.096700I
a = 0.615073 + 0.266917I
b = −1.40828 + 0.31772I
6.45837 − 5.82425I 0
u = 0.183709 − 1.096700I
a = 0.615073 − 0.266917I
b = −1.40828 − 0.31772I
6.45837 + 5.82425I 0
u = −0.060804 + 1.151400I
a = −0.235310 − 0.453905I
b = 1.07199 − 1.72723I
10.49640 + 2.30207I 0
u = −0.060804 − 1.151400I
a = −0.235310 + 0.453905I
b = 1.07199 + 1.72723I
10.49640 − 2.30207I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697220 + 0.415437I
a = 0.367510 − 0.569917I
b = 0.598266 + 0.118968I
2.58042 + 2.27566I 5.54808 − 4.42595I
u = −0.697220 − 0.415437I
a = 0.367510 + 0.569917I
b = 0.598266 − 0.118968I
2.58042 − 2.27566I 5.54808 + 4.42595I
u = 0.348979 + 1.163470I
a = −0.789223 − 0.400014I
b = 0.803943 + 0.133985I
12.4109 − 11.7818I 0
u = 0.348979 − 1.163470I
a = −0.789223 + 0.400014I
b = 0.803943 − 0.133985I
12.4109 + 11.7818I 0
u = 0.400033 + 1.148970I
a = −0.209336 − 0.368266I
b = 0.537132 + 0.552257I
11.91410 + 0.46291I 0
u = 0.400033 − 1.148970I
a = −0.209336 + 0.368266I
b = 0.537132 − 0.552257I
11.91410 − 0.46291I 0
u = 0.638183 + 0.414259I
a = −0.885666 − 0.562368I
b = −0.877415 + 0.319431I
7.44710 − 8.39986I 4.21700 + 7.17865I
u = 0.638183 − 0.414259I
a = −0.885666 + 0.562368I
b = −0.877415 − 0.319431I
7.44710 + 8.39986I 4.21700 − 7.17865I
u = 0.673423 + 0.351163I
a = −0.043002 − 1.043460I
b = −0.615958 − 0.222480I
7.23787 + 4.15053I 4.88455 − 1.78073I
u = 0.673423 − 0.351163I
a = −0.043002 + 1.043460I
b = −0.615958 + 0.222480I
7.23787 − 4.15053I 4.88455 + 1.78073I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369763 + 1.185950I
a = 0.519790 − 0.236280I
b = −0.595932 + 0.252414I
7.64201 + 5.93448I 0
u = −0.369763 − 1.185950I
a = 0.519790 + 0.236280I
b = −0.595932 − 0.252414I
7.64201 − 5.93448I 0
u = −0.284491 + 0.620702I
a = 0.089749 + 0.451278I
b = 0.078976 + 0.540092I
0.33460 + 1.76623I −3.26918 − 5.78660I
u = −0.284491 − 0.620702I
a = 0.089749 − 0.451278I
b = 0.078976 − 0.540092I
0.33460 − 1.76623I −3.26918 + 5.78660I
u = 0.392790 + 0.323030I
a = 2.01412 + 0.72401I
b = 0.535471 − 0.302352I
1.98439 − 3.87908I 1.02310 + 8.63789I
u = 0.392790 − 0.323030I
a = 2.01412 − 0.72401I
b = 0.535471 + 0.302352I
1.98439 + 3.87908I 1.02310 − 8.63789I
u = −0.166207 + 0.454728I
a = −1.06595 + 3.13668I
b = −0.335420 − 0.115389I
5.39007 + 1.57476I 8.26638 − 4.56003I
u = −0.166207 − 0.454728I
a = −1.06595 − 3.13668I
b = −0.335420 + 0.115389I
5.39007 − 1.57476I 8.26638 + 4.56003I
u = −0.400179 + 0.184061I
a = −1.113230 + 0.254594I
b = −0.294175 − 0.144169I
−0.906294 + 0.638936I −7.84585 − 3.54441I
u = −0.400179 − 0.184061I
a = −1.113230 − 0.254594I
b = −0.294175 + 0.144169I
−0.906294 − 0.638936I −7.84585 + 3.54441I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.337976 + 0.277219I
a = 0.080619 + 1.061220I
b = 0.612117 + 0.741472I
1.91837 + 1.38671I 0.37102 + 1.92125I
u = 0.337976 − 0.277219I
a = 0.080619 − 1.061220I
b = 0.612117 − 0.741472I
1.91837 − 1.38671I 0.37102 − 1.92125I
u = −0.08231 + 1.59104I
a = 0.098365 + 0.362333I
b = 0.061723 + 0.202369I
7.93934 + 3.04380I 0
u = −0.08231 − 1.59104I
a = 0.098365 − 0.362333I
b = 0.061723 − 0.202369I
7.93934 − 3.04380I 0
u = −0.309511
a = −0.285999
b = −1.99031
3.96788 −11.2160
u = 0.146397 + 0.259785I
a = 0.26789 + 2.10948I
b = 0.661555 − 0.546534I
1.70235 − 0.53525I 5.77546 − 2.21892I
u = 0.146397 − 0.259785I
a = 0.26789 − 2.10948I
b = 0.661555 + 0.546534I
1.70235 + 0.53525I 5.77546 + 2.21892I
u = 0.02066 + 1.73571I
a = −2.64807 − 1.49652I
b = −5.03892 − 2.83332I
15.7407 − 0.4328I 0
u = 0.02066 − 1.73571I
a = −2.64807 + 1.49652I
b = −5.03892 + 2.83332I
15.7407 + 0.4328I 0
u = −0.03957 + 1.74066I
a = 2.21887 − 0.02192I
b = 3.84932 − 0.12795I
12.88280 + 3.36516I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03957 − 1.74066I
a = 2.21887 + 0.02192I
b = 3.84932 + 0.12795I
12.88280 − 3.36516I 0
u = 0.00922 + 1.75210I
a = −1.76414 + 0.35710I
b = −3.28376 + 1.33114I
16.2367 − 1.3130I 0
u = 0.00922 − 1.75210I
a = −1.76414 − 0.35710I
b = −3.28376 − 1.33114I
16.2367 + 1.3130I 0
u = 0.04422 + 1.75495I
a = −2.98121 + 0.32099I
b = −4.98803 + 0.54697I
16.7715 − 6.7678I 0
u = 0.04422 − 1.75495I
a = −2.98121 − 0.32099I
b = −4.98803 − 0.54697I
16.7715 + 6.7678I 0
u = −0.01406 + 1.76783I
a = 1.92068 − 1.63644I
b = 3.22687 − 2.19591I
−18.3521 + 2.6162I 0
u = −0.01406 − 1.76783I
a = 1.92068 + 1.63644I
b = 3.22687 + 2.19591I
−18.3521 − 2.6162I 0
u = 0.09238 + 1.77000I
a = 2.54868 + 0.19679I
b = 4.60054 + 0.16183I
−16.5345 − 13.6959I 0
u = 0.09238 − 1.77000I
a = 2.54868 − 0.19679I
b = 4.60054 − 0.16183I
−16.5345 + 13.6959I 0
u = 0.10675 + 1.77331I
a = 1.50063 + 0.72497I
b = 2.72216 + 1.03571I
−17.0899 − 1.7379I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10675 − 1.77331I
a = 1.50063 − 0.72497I
b = 2.72216 − 1.03571I
−17.0899 + 1.7379I 0
u = −0.09538 + 1.77635I
a = −1.97891 + 0.19640I
b = −3.58909 + 0.12592I
18.2869 + 7.9543I 0
u = −0.09538 − 1.77635I
a = −1.97891 − 0.19640I
b = −3.58909 − 0.12592I
18.2869 − 7.9543I 0
10
II.
I
u
2
= hu
3
+ 2u
2
+ 4b + 5u + 3, −5u
3
− 2u
2
+ 8a − 9u − 3, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
5
8
u
3
+
1
4
u
2
+
9
8
u +
3
8
−
1
4
u
3
−
1
2
u
2
−
5
4
u −
3
4
a
10
=
5
8
u
3
+
1
4
u
2
+
9
8
u +
3
8
−
1
4
u
3
−
1
2
u
2
−
5
4
u −
3
4
a
3
=
0.109375u
3
+ 0.0937500u
2
+ 0.171875u + 0.765625
0.0312500u
3
− 0.687500u
2
− 0.0937500u + 0.218750
a
12
=
u
u
a
6
=
u
2
+ 1
u
2
a
7
=
0.296875u
3
+ 0.968750u
2
+ 0.609375u + 1.07813
−0.343750u
3
+ 0.562500u
2
− 0.968750u − 0.406250
a
11
=
u
3
+ 2u
u
3
+ u
a
8
=
−
3
8
u
3
+
1
4
u
2
−
7
8
u +
3
8
−
5
4
u
3
−
1
2
u
2
−
9
4
u −
3
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
233
64
u
3
−
205
32
u
2
−
805
64
u −
159
64
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
, c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
8(8u
4
+ 3u
3
+ 6u
2
+ u + 1)
c
4
, c
5
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
6
8(8u
4
+ 15u
3
+ 12u
2
+ 5u + 1)
c
7
u
4
+ u
3
+ u
2
+ 1
c
8
(u + 1)
4
c
9
u
4
c
10
(u − 1)
4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
7
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
64(64y
4
+ 87y
3
+ 46y
2
+ 11y + 1)
c
6
64(64y
4
− 33y
3
+ 10y
2
− y + 1)
c
8
, c
10
(y −1)
4
c
9
y
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0.057058 + 0.537058I
b = −0.266417 − 0.460085I
1.43393 + 1.41510I 2.24706 − 4.19946I
u = −0.395123 − 0.506844I
a = 0.057058 − 0.537058I
b = −0.266417 + 0.460085I
1.43393 − 1.41510I 2.24706 + 4.19946I
u = −0.10488 + 1.55249I
a = 0.130442 − 0.641504I
b = 0.391417 − 0.855136I
8.43568 + 3.16396I 11.44826 − 4.00508I
u = −0.10488 − 1.55249I
a = 0.130442 + 0.641504I
b = 0.391417 + 0.855136I
8.43568 − 3.16396I 11.44826 + 4.00508I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
53
− 2u
52
+ ··· − 3u + 1)
c
2
(u
4
− u
3
+ u
2
+ 1)(u
53
+ 2u
52
+ ··· + 3u − 1)
c
3
64(8u
4
+ 3u
3
+ ··· + u + 1)(8u
53
− 11u
52
+ ··· + 480u + 3943)
c
4
, c
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
53
− 2u
52
+ ··· − 3u + 1)
c
6
64(8u
4
+ 15u
3
+ 12u
2
+ 5u + 1)
· (8u
53
− 7u
52
+ ··· + 348462u + 61297)
c
7
(u
4
+ u
3
+ u
2
+ 1)(u
53
+ 2u
52
+ ··· + 3u − 1)
c
8
((u + 1)
4
)(u
53
+ 5u
52
+ ··· − 17u − 64)
c
9
u
4
(u
53
− 3u
52
+ ··· − 576u + 1024)
c
10
((u − 1)
4
)(u
53
+ 5u
52
+ ··· − 17u − 64)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
53
+ 72y
52
+ ··· − 13y −1)
c
2
, c
7
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
53
− 36y
52
+ ··· − 13y −1)
c
3
4096(64y
4
+ 87y
3
+ 46y
2
+ 11y + 1)
· (64y
53
+ 2007y
52
+ ··· − 99819282y −15547249)
c
6
4096(64y
4
− 33y
3
+ 10y
2
− y + 1)
· (64y
53
− 3105y
52
+ ··· + 24414558770y −3757322209)
c
8
, c
10
((y −1)
4
)(y
53
− 49y
52
+ ··· + 68129y −4096)
c
9
y
4
(y
53
+ 27y
52
+ ··· − 8925184y −1048576)
16
