Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.12.16.23 |
$12$ |
$x^{12} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$16$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[4/3, 5/3]$ |
$[4/3, 4/3, 5/3, 5/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1, 2]$ |
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) |
$2$ |
$3$ |
$[4/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{5} + 2 x^{2} + 2$ |
$[11, 2, 0]$ |
$[1, 1, 2]$ |
2.12.32.224 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 4 x^{2} + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
2.12.32.280 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
2.12.32.387 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 12 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |
2.12.32.389 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$12$ |
$1$ |
$32$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[8/3, 11/3]$ |
$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{3} + 4 x^{2} + 10$ |
$[21, 10, 0]$ |
$[1, 1, 2]$ |