| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.18.73 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$18$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[4/3, 2]$ |
$[4/3, 4/3, 5/3, 5/3, 2]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{2} + 2$ |
$[7, 2, 0]$ |
$[1, 1, 2]$ |
| 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) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.24.358 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$24$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[4/3, 3]$ |
$[4/3, 4/3, 5/3, 5/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$[13, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.24.382 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 2 x^{2} + 4 x + 2$ |
$2$ |
$12$ |
$1$ |
$24$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[4/3, 3]$ |
$[4/3, 4/3, 5/3, 5/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 2 x^{8} + 2 x^{2} + 4 x + 2$ |
$[13, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.24.385 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 6 x^{6} + 4 x^{4} + 2 x^{2} + 4 x + 14$ |
$2$ |
$12$ |
$1$ |
$24$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[4/3, 3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 6 x^{6} + 4 x^{4} + 2 x^{2} + 4 x + 14$ |
$[13, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.24.415 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 6 x^{2} + 4 x + 10$ |
$2$ |
$12$ |
$1$ |
$24$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[4/3, 3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 2 x^{6} + 6 x^{2} + 4 x + 10$ |
$[13, 2, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.1 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 12 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 12 x^{2} + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.184 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.295 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.33 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{6} + 12 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{6} + 12 x^{2} + 8 x + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.435 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.452 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{6} + 12 x^{2} + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.463 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{6} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{6} + 12 x^{2} + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.474 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.511 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{6} + 8 x^{5} + 8 x^{4} + 12 x^{2} + 8 x + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.535 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{6} + 12 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{6} + 12 x^{2} + 8 x + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.55 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 12 x^{6} + 12 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 12 x^{6} + 12 x^{2} + 8 x + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
| 2.12.32.86 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 12 x^{2} + 8 x + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 12 x^{2} + 8 x + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
