| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.26.1 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.10 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.100 |
$12$ |
$x^{12} + 2 x^{10} + 6 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 6 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.101 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.102 |
$12$ |
$x^{12} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.103 |
$12$ |
$x^{12} + 4 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.104 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.105 |
$12$ |
$x^{12} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$A_4:C_4$ (as 12T27) |
$4$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3]_{3}^{4}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.106 |
$12$ |
$x^{12} + 4 x^{7} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2:S_4$ (as 12T66) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 4 x^{3} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.107 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.108 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.109 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{8} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T52) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 2 x^{8} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.11 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.110 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.111 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.112 |
$12$ |
$x^{12} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.113 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.114 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.115 |
$12$ |
$x^{12} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.116 |
$12$ |
$x^{12} + 4 x^{9} + 6 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 6 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.117 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 14$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 14$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.118 |
$12$ |
$x^{12} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.119 |
$12$ |
$x^{12} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^3.S_4$ (as 12T102) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.12 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.120 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.121 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T52) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.122 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\wr S_3$ (as 12T139) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.123 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.124 |
$12$ |
$x^{12} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.125 |
$12$ |
$x^{12} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2:S_4$ (as 12T66) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.126 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.127 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.128 |
$12$ |
$x^{12} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.13 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.14 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.15 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.16 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.17 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T136) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.18 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 4 x^{2} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.19 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 6 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.2 |
$12$ |
$x^{12} + 4 x^{7} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2\wr S_3$ (as 12T148) |
$2$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 12, 0]$ |
$[2, 2]$ |
| 2.12.26.20 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 2 x^{6} + 4 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\wr S_3$ (as 12T139) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 2 x^{6} + 4 x^{3} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.21 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T147) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 6 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.22 |
$12$ |
$x^{12} + 4 x^{10} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 2 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.23 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{6} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\wr S_3$ (as 12T139) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{6} + 4 x^{3} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.24 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4.S_4$ (as 12T138) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{3} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.25 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{7} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:(S_3\times A_4)$ (as 12T206) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{7} + 4 x^{3} + 2$ |
$[15, 10, 0]$ |
$[3, 2]$ |
| 2.12.26.26 |
$12$ |
$x^{12} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4.S_4$ (as 12T138) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.27 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^2\times S_4$ (as 12T48) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.28 |
$12$ |
$x^{12} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$C_2^4:S_4$ (as 12T145) |
$2$ |
$3$ |
$[2, 3]$ |
$[4/3, 4/3, 2, 7/3, 7/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{7} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
