| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.22.1 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 8 x^{9} + 16 x^{8} - 28 x^{7} + 56 x^{6} + 64 x^{5} + 36 x^{4} - 24 x^{3} + 16 x^{2} + 72 x + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 6 x^{2} + 4 t x + 12 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.10 |
$12$ |
$x^{12} + 4 x^{10} + 6 x^{8} + 8 x^{7} + 22 x^{6} + 16 x^{5} + 64 x^{4} + 8 x^{3} + 88 x^{2} + 72 x + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + \left(6 t + 4\right) x^{2} + 4 x + 6 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.100 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[20/9, 20/9]$ |
$[20/9, 20/9, 20/9, 20/9, 20/9, 20/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 4 x^{3} + 4 x^{2} + 2$ |
$[11, 10, 0]$ |
$[1, 2]$ |
| 2.12.22.101 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{3} + 4 x^{2} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[20/9, 20/9]$ |
$[20/9, 20/9, 20/9, 20/9, 20/9, 20/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{3} + 4 x^{2} + 4 x + 2$ |
$[11, 11, 0]$ |
$[1, 2]$ |
| 2.12.22.102 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 4 x^{3} + 4 x^{2} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[20/9, 20/9]$ |
$[20/9, 20/9, 20/9, 20/9, 20/9, 20/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 4 x^{3} + 4 x^{2} + 4 x + 6$ |
$[11, 10, 0]$ |
$[1, 2]$ |
| 2.12.22.103 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T103) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.104 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 6 x^{2} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T149) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 6 x^{2} + 4 x + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.105 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 6 x^{6} + 4 x^{4} + 2 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T149) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 6 x^{6} + 4 x^{4} + 2 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.106 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 6 x^{4} + 4 x^{3} + 6 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2:S_4$ (as 12T67) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 6 x^{4} + 4 x^{3} + 6 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.107 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T149) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.108 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x^{4} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x^{4} + 4 x + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.109 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:D_6$ (as 12T112) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.11 |
$12$ |
$x^{12} + 8 x^{10} + 32 x^{8} + 4 x^{7} + 2 x^{6} + 40 x^{5} + 32 x^{4} + 8 x^{3} - 12 x^{2} + 56 x + 196$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[3]$ |
$[2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 14 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.110 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 6 x^{4} + 6 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T110) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 6 x^{4} + 6 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.111 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.112 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:D_6$ (as 12T113) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.113 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T110) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.114 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T147) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 6$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.115 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2:S_4$ (as 12T68) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.116 |
$12$ |
$x^{12} + 2 x^{11} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[20/9, 20/9]$ |
$[20/9, 20/9, 20/9, 20/9, 20/9, 20/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x + 2$ |
$[11, 11, 0]$ |
$[1, 2]$ |
| 2.12.22.117 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T103) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{3} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.118 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.119 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x + 6$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.12 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 12 x^{9} + 36 x^{8} - 12 x^{7} + 76 x^{6} - 64 x^{5} + 88 x^{4} - 56 x^{3} + 16 x^{2} - 56 x + 196$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2^3:S_4$ (as 12T106) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 4 t x^{3} + 4 t x + 14$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.120 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3.S_4$ (as 12T102) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 6 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.121 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:D_6$ (as 12T95) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 6 x^{6} + 6 x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.122 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T147) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.123 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x^{4} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{6} + 4 x^{4} + 6$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.124 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{5} + 2 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3.S_4$ (as 12T98) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{5} + 2 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.125 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T147) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x + 6$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.126 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^4:S_4$ (as 12T146) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.127 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[20/9, 20/9]$ |
$[20/9, 20/9, 20/9, 20/9, 20/9, 20/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 4 x^{2} + 6$ |
$[11, 10, 0]$ |
$[1, 2]$ |
| 2.12.22.128 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T100) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{4} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.129 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 2 x^{2} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T111) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 2 x^{2} + 4 x + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.13 |
$12$ |
$x^{12} + 4 x^{11} + 28 x^{10} + 20 x^{9} + 64 x^{8} - 4 x^{7} + 122 x^{6} + 24 x^{5} + 176 x^{4} - 24 x^{3} + 124 x^{2} + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 4\right) x^{5} + 6 x^{4} + 4 t x^{3} + 6 x^{2} + 4 t x + 6 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.130 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T108) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.131 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.132 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T111) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.133 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:D_6$ (as 12T96) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.134 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{4} + 6 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2:S_4$ (as 12T66) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 6 x^{8} + 4 x^{7} + 2 x^{4} + 6 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.135 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T147) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 2 x^{6} + 4 x + 2$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.136 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{3} + 4 x + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:D_6$ (as 12T112) |
$2$ |
$3$ |
$[2, 7/3]$ |
$[4/3, 4/3, 2, 7/3, 7/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{3} + 4 x + 6$ |
$[11, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.137 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:D_6$ (as 12T95) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.138 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:S_3$ (as 12T63) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 4 x + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.139 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{5} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{5} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.14 |
$12$ |
$x^{12} + 8 x^{10} + 40 x^{8} + 62 x^{6} + 152 x^{4} + 84 x^{2} + 124$ |
$2$ |
$6$ |
$2$ |
$22$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[3]$ |
$[2, 8/3, 8/3, 8/3, 8/3, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + 6 x^{2} + 10 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.140 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^2:S_4$ (as 12T68) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.141 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 6 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3.S_4$ (as 12T98) |
$4$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{4}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 6 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.142 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3.S_4$ (as 12T98) |
$4$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{4}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.22.143 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 2 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$22$ |
$C_2^3:S_4$ (as 12T101) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 2 x^{2} + 6$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
