| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.29.147 |
$12$ |
$x^{12} + 10 x^{6} + 6$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 10 x^{6} + 6$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.29.217 |
$12$ |
$x^{12} + 2 x^{6} + 8 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{6} + 8 x^{3} + 6$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.29.229 |
$12$ |
$x^{12} + 10 x^{6} + 8 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 10 x^{6} + 8 x^{3} + 2$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.29.247 |
$12$ |
$x^{12} + 2 x^{6} + 6$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{6} + 6$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.29.25 |
$12$ |
$x^{12} + 10 x^{6} + 2$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 10 x^{6} + 2$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.29.27 |
$12$ |
$x^{12} + 2 x^{6} + 2$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{6} + 2$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.29.34 |
$12$ |
$x^{12} + 10 x^{6} + 8 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 10 x^{6} + 8 x^{3} + 6$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.29.51 |
$12$ |
$x^{12} + 4 x^{9} + 14 x^{6} + 10$ |
$2$ |
$12$ |
$1$ |
$29$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[2, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 14 x^{6} + 10$ |
$[18, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.111 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{4} + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{4} + 2$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.146 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 12 x^{4} + 8 x^{2} + 8 x + 14$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 12 x^{4} + 8 x^{2} + 8 x + 14$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.148 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{8} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 10$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.186 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 12 x^{4} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 12 x^{4} + 8 x + 2$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.301 |
$12$ |
$x^{12} + 4 x^{9} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 10$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.429 |
$12$ |
$x^{12} + 4 x^{9} + 4 x^{6} + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 4 x^{6} + 2$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.48 |
$12$ |
$x^{12} + 4 x^{9} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 12 x^{6} + 8 x^{5} + 8 x^{4} + 8 x^{2} + 2$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.83 |
$12$ |
$x^{12} + 4 x^{9} + 8 x^{6} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 7/2]$ |
$[2, 3, 7/2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{9} + 8 x^{6} + 10$ |
$[21, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.109 |
$12$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 2$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.180 |
$12$ |
$x^{12} + 10$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 10$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.330 |
$12$ |
$x^{12} + 8 x^{11} + 12 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 12 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.559 |
$12$ |
$x^{12} + 8 x^{11} + 12 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 8 x^{11} + 12 x^{10} + 8 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.57 |
$12$ |
$x^{12} + 26$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 26$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.796 |
$12$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 18$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 18$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.878 |
$12$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 26$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 26$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
| 2.12.35.980 |
$12$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$35$ |
$S_3\times D_4$ (as 12T28) |
$2$ |
$3$ |
$[3, 4]$ |
$[2, 3, 4]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 8 x^{3} + 10$ |
$[24, 12, 0]$ |
$[1, 1, 2]$ |
