29241.1-a1
29241.1-a
4 4 4
4 4 4
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 14 ⋅ 1 9 8 3^{14} \cdot 19^{8} 3 1 4 ⋅ 1 9 8
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
0
Z / 4 Z \Z/4\Z Z / 4 Z
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
2 2 2
2B
4 4 4
2 4 2^{4} 2 4
1 1 1
0.544114833 0.544114833 0 . 5 4 4 1 1 4 8 3 3
2.176459332
67419143 390963 \frac{67419143}{390963} 3 9 0 9 6 3 6 7 4 1 9 1 4 3
[ i \bigl[i [ i , 1 1 1 , i i i , 77 77 7 7 , 790 ] 790\bigr] 7 9 0 ]
y 2 + i x y + i y = x 3 + x 2 + 77 x + 790 {y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+77{x}+790 y 2 + i x y + i y = x 3 + x 2 + 7 7 x + 7 9 0
29241.1-a2
29241.1-a
4 4 4
4 4 4
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 14 ⋅ 1 9 2 3^{14} \cdot 19^{2} 3 1 4 ⋅ 1 9 2
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
0
Z / 4 Z \Z/4\Z Z / 4 Z
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
2 2 2
2B
4 4 4
2 2 2^{2} 2 2
1 1 1
2.176459332 2.176459332 2 . 1 7 6 4 5 9 3 3 2
2.176459332
389017 57 \frac{389017}{57} 5 7 3 8 9 0 1 7
[ i \bigl[i [ i , 1 1 1 , i i i , − 13 -13 − 1 3 , − 20 ] -20\bigr] − 2 0 ]
y 2 + i x y + i y = x 3 + x 2 − 13 x − 20 {y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-13{x}-20 y 2 + i x y + i y = x 3 + x 2 − 1 3 x − 2 0
29241.1-a3
29241.1-a
4 4 4
4 4 4
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 16 ⋅ 1 9 4 3^{16} \cdot 19^{4} 3 1 6 ⋅ 1 9 4
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
0
Z / 2 Z ⊕ Z / 2 Z \Z/2\Z\oplus\Z/2\Z Z / 2 Z ⊕ Z / 2 Z
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
2 2 2
2Cs
4 4 4
2 3 2^{3} 2 3
1 1 1
1.088229666 1.088229666 1 . 0 8 8 2 2 9 6 6 6
2.176459332
30664297 3249 \frac{30664297}{3249} 3 2 4 9 3 0 6 6 4 2 9 7
[ i \bigl[i [ i , 1 1 1 , i i i , − 58 -58 − 5 8 , 142 ] 142\bigr] 1 4 2 ]
y 2 + i x y + i y = x 3 + x 2 − 58 x + 142 {y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-58{x}+142 y 2 + i x y + i y = x 3 + x 2 − 5 8 x + 1 4 2
29241.1-a4
29241.1-a
4 4 4
4 4 4
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 20 ⋅ 1 9 2 3^{20} \cdot 19^{2} 3 2 0 ⋅ 1 9 2
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
0
Z / 2 Z \Z/2\Z Z / 2 Z
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
2 2 2
2B
4 4 4
2 2 2^{2} 2 2
1 1 1
0.544114833 0.544114833 0 . 5 4 4 1 1 4 8 3 3
2.176459332
115714886617 1539 \frac{115714886617}{1539} 1 5 3 9 1 1 5 7 1 4 8 8 6 6 1 7
[ i \bigl[i [ i , 1 1 1 , i i i , − 913 -913 − 9 1 3 , 10402 ] 10402\bigr] 1 0 4 0 2 ]
y 2 + i x y + i y = x 3 + x 2 − 913 x + 10402 {y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-913{x}+10402 y 2 + i x y + i y = x 3 + x 2 − 9 1 3 x + 1 0 4 0 2
29241.1-b1
29241.1-b
3 3 3
9 9 9
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 12 ⋅ 1 9 2 3^{12} \cdot 19^{2} 3 1 2 ⋅ 1 9 2
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
2 2 2
Z / 3 Z \Z/3\Z Z / 3 Z
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
3 3 3
3B.1.1
1 1 1
2 2 2^{2} 2 2
5.606459454 5.606459454 5 . 6 0 6 4 5 9 4 5 4
0.311769669 0.311769669 0 . 3 1 1 7 6 9 6 6 9
3.107420464
− 50357871050752 19 -\frac{50357871050752}{19} − 1 9 5 0 3 5 7 8 7 1 0 5 0 7 5 2
[ 0 \bigl[0 [ 0 , 0 0 0 , i i i , − 6924 -6924 − 6 9 2 4 , − 221760 ] -221760\bigr] − 2 2 1 7 6 0 ]
y 2 + i y = x 3 − 6924 x − 221760 {y}^2+i{y}={x}^{3}-6924{x}-221760 y 2 + i y = x 3 − 6 9 2 4 x − 2 2 1 7 6 0
29241.1-b2
29241.1-b
3 3 3
9 9 9
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 12 ⋅ 1 9 6 3^{12} \cdot 19^{6} 3 1 2 ⋅ 1 9 6
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
2 2 2
Z / 3 Z \Z/3\Z Z / 3 Z
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
3 3 3
3Cs.1.1
1 1 1
2 2 ⋅ 3 2^{2} \cdot 3 2 2 ⋅ 3
0.622939939 0.622939939 0 . 6 2 2 9 3 9 9 3 9
0.935309008 0.935309008 0 . 9 3 5 3 0 9 0 0 8
3.107420464
− 89915392 6859 -\frac{89915392}{6859} − 6 8 5 9 8 9 9 1 5 3 9 2
[ 0 \bigl[0 [ 0 , 0 0 0 , i i i , − 84 -84 − 8 4 , − 315 ] -315\bigr] − 3 1 5 ]
y 2 + i y = x 3 − 84 x − 315 {y}^2+i{y}={x}^{3}-84{x}-315 y 2 + i y = x 3 − 8 4 x − 3 1 5
29241.1-b3
29241.1-b
3 3 3
9 9 9
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 12 ⋅ 1 9 2 3^{12} \cdot 19^{2} 3 1 2 ⋅ 1 9 2
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
2 2 2
t r i v i a l \mathsf{trivial} t r i v i a l
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
3 3 3
3B.1.2
1 1 1
2 2 2^{2} 2 2
0.069215548 0.069215548 0 . 0 6 9 2 1 5 5 4 8
2.805927025 2.805927025 2 . 8 0 5 9 2 7 0 2 5
3.107420464
32768 19 \frac{32768}{19} 1 9 3 2 7 6 8
[ 0 \bigl[0 [ 0 , 0 0 0 , i i i , 6 6 6 , 0 ] 0\bigr] 0 ]
y 2 + i y = x 3 + 6 x {y}^2+i{y}={x}^{3}+6{x} y 2 + i y = x 3 + 6 x
29241.1-c1
29241.1-c
2 2 2
5 5 5
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 16 ⋅ 1 9 10 3^{16} \cdot 19^{10} 3 1 6 ⋅ 1 9 1 0
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
0
t r i v i a l \mathsf{trivial} t r i v i a l
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
5 5 5
5B.4.2
1 1 1
2 2 ⋅ 5 2^{2} \cdot 5 2 2 ⋅ 5
1 1 1
0.090588610 0.090588610 0 . 0 9 0 5 8 8 6 1 0
1.811772200
− 9358714467168256 22284891 -\frac{9358714467168256}{22284891} − 2 2 2 8 4 8 9 1 9 3 5 8 7 1 4 4 6 7 1 6 8 2 5 6
[ 0 \bigl[0 [ 0 , 0 0 0 , 1 1 1 , − 39513 -39513 − 3 9 5 1 3 , 3023145 ] 3023145\bigr] 3 0 2 3 1 4 5 ]
y 2 + y = x 3 − 39513 x + 3023145 {y}^2+{y}={x}^{3}-39513{x}+3023145 y 2 + y = x 3 − 3 9 5 1 3 x + 3 0 2 3 1 4 5
29241.1-c2
29241.1-c
2 2 2
5 5 5
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 32 ⋅ 1 9 2 3^{32} \cdot 19^{2} 3 3 2 ⋅ 1 9 2
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
0
t r i v i a l \mathsf{trivial} t r i v i a l
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
5 5 5
5B.4.1
1 1 1
2 2 2^{2} 2 2
1 1 1
0.452943050 0.452943050 0 . 4 5 2 9 4 3 0 5 0
1.811772200
841232384 1121931 \frac{841232384}{1121931} 1 1 2 1 9 3 1 8 4 1 2 3 2 3 8 4
[ 0 \bigl[0 [ 0 , 0 0 0 , i i i , 177 177 1 7 7 , − 1035 ] -1035\bigr] − 1 0 3 5 ]
y 2 + i y = x 3 + 177 x − 1035 {y}^2+i{y}={x}^{3}+177{x}-1035 y 2 + i y = x 3 + 1 7 7 x − 1 0 3 5
29241.1-d1
29241.1-d
1 1 1
1 1 1
Q ( − 1 ) \Q(\sqrt{-1}) Q ( − 1 )
2 2 2
[ 0 , 1 ] [0, 1] [ 0 , 1 ]
29241.1
3 4 ⋅ 1 9 2 3^{4} \cdot 19^{2} 3 4 ⋅ 1 9 2
3 16 ⋅ 1 9 2 3^{16} \cdot 19^{2} 3 1 6 ⋅ 1 9 2
2.33704 2.33704 2 . 3 3 7 0 4
( 3 ) , ( 19 ) (3), (19) ( 3 ) , ( 1 9 )
0
t r i v i a l \mathsf{trivial} t r i v i a l
no \textsf{no} no
S U ( 2 ) \mathrm{SU}(2) S U ( 2 )
✓
✓
1 1 1
2 2 2^{2} 2 2
1 1 1
1.776214705 1.776214705 1 . 7 7 6 2 1 4 7 0 5
7.104858821
− 1404928 171 -\frac{1404928}{171} − 1 7 1 1 4 0 4 9 2 8
[ 0 \bigl[0 [ 0 , 0 0 0 , i i i , − 21 -21 − 2 1 , 41 ] 41\bigr] 4 1 ]
y 2 + i y = x 3 − 21 x + 41 {y}^2+i{y}={x}^{3}-21{x}+41 y 2 + i y = x 3 − 2 1 x + 4 1