| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.26.45 |
$12$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$ |
$2$ |
$12$ |
$1$ |
$26$ |
$S_3 \times C_2^2$ (as 12T10) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 2 x^{10} + 6 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 14$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.64 |
$12$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$26$ |
$S_3 \times C_2^2$ (as 12T10) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 4 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 2$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.72 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{6} + 4 x^{3} + 10$ |
$2$ |
$12$ |
$1$ |
$26$ |
$S_3 \times C_2^2$ (as 12T10) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{6} + 4 x^{3} + 10$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
| 2.12.26.99 |
$12$ |
$x^{12} + 6 x^{6} + 4 x^{3} + 6$ |
$2$ |
$12$ |
$1$ |
$26$ |
$S_3 \times C_2^2$ (as 12T10) |
$2$ |
$3$ |
$[2, 3]$ |
$[2, 3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 4 x^{3} + 6$ |
$[15, 6, 0]$ |
$[1, 1, 2]$ |
