| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.8.1 |
$12$ |
$x^{12} + 11 x^{9} + 3 x^{8} - 9 x^{6} - 90 x^{5} + 3 x^{4} - 27 x^{3} + 135 x^{2} + 27 x + 55$ |
$2$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$t^{4} + t + 1$ |
$x^{3} + 2$ |
$[0]$ |
$[1]$ |
| 2.12.16.18 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.22.63 |
$12$ |
$x^{12} + 8 x^{11} + 20 x^{10} + 16 x^{9} + 8 x^{8} + 24 x^{7} + 52 x^{6} + 64 x^{5} + 28 x^{4} + 16 x^{3} + 40 x^{2} + 48 x + 84$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$3$ |
$[3]$ |
$[3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 2 x^{4} + 2 x^{2} + 4 x + 8 t + 10$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.80 |
$12$ |
$x^{12} + 8 x^{11} + 20 x^{10} + 24 x^{9} + 40 x^{8} + 40 x^{7} + 52 x^{6} + 16 x^{5} + 28 x^{4} + 8 x^{2} - 16 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$3$ |
$[3]$ |
$[3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 8 t + 2$ |
$[6, 0]$ |
$[1, 1]$ |
