| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.34.1 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 12 x^{6} + 8 x^{3} + 8 x^{2} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.10 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^4.S_4$ (as 12T138) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.100 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.101 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.102 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 8 x + 14$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{5} + 8 x^{4} + 4 x^{2} + 8 x + 14$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.103 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.104 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr D_6$ (as 12T193) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{8} + 4 x^{6} + 8 x^{3} + 8 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.105 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 12 x^{6} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 12 x^{6} + 12 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.106 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{3} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.107 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 8 x^{8} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 8 x^{8} + 8 x^{3} + 8 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.108 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{5} + 4 x^{4} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{5} + 4 x^{4} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.109 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{9} + 12 x^{8} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{9} + 12 x^{8} + 12 x^{6} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.11 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.110 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.111 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 8 x^{7} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.112 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{2} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.113 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{7} + 12 x^{4} + 8 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^3:S_4$ (as 12T108) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{7} + 12 x^{4} + 8 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.114 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 12 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 8 x + 6$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 12 x^{8} + 8 x^{5} + 12 x^{4} + 12 x^{2} + 8 x + 6$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.115 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 12 x^{8} + 12 x^{6} + 8 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr D_6$ (as 12T193) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 12 x^{8} + 12 x^{6} + 8 x^{4} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.116 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.117 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr D_6$ (as 12T193) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.118 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 12 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.119 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{8} + 4 x^{6} + 8 x^{5} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.12 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.120 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 12 x^{4} + 8 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.121 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{4} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{4} + 8 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.122 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.123 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.124 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 8 x^{6} + 8 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.125 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 4 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{4} + 12 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.126 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.127 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_4^3:D_6$ (as 12T185) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.128 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.129 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{8} + 8 x^{5} + 4 x^{4} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{8} + 8 x^{5} + 4 x^{4} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.13 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{5} + 8 x^{4} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr D_6$ (as 12T193) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{5} + 8 x^{4} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.130 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 4 x^{4} + 8 x^{2} + 8 x + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.131 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 12 x^{8} + 8 x^{7} + 4 x^{6} + 12 x^{2} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.132 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{8} + 12 x^{2} + 8 x + 6$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{8} + 12 x^{2} + 8 x + 6$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.133 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr D_6$ (as 12T193) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{9} + 8 x^{8} + 8 x^{4} + 8 x^{3} + 8 x^{2} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.134 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 8 x^{8} + 8 x^{5} + 12 x^{4} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.135 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_4^3:D_6$ (as 12T185) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.136 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 12 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.137 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{8} + 8 x^{6} + 4 x^{4} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{8} + 8 x^{6} + 4 x^{4} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.138 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.139 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr D_6$ (as 12T193) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{7} + 4 x^{6} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.14 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 8 x + 6$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 8 x + 6$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.140 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 8 x^{6} + 8 x^{4} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr D_6$ (as 12T193) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[2, 8/3, 8/3, 3, 7/2, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{8} + 8 x^{6} + 8 x^{4} + 8 x^{2} + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.141 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{8} + 12 x^{4} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2\wr S_4$ (as 12T223) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[4/3, 4/3, 8/3, 8/3, 3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 12 x^{8} + 12 x^{4} + 12 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.142 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 12 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_2^3:S_4$ (as 12T109) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 12 x^{8} + 4 x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 2$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.34.143 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$34$ |
$C_4^2:D_6$ (as 12T113) |
$2$ |
$3$ |
$[3, 23/6]$ |
$[8/3, 8/3, 3, 23/6, 23/6]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 8 x^{5} + 4 x^{4} + 4 x^{2} + 10$ |
$[23, 12, 0]$ |
$[1, 1, 2]$ |
