| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.16.2 |
$12$ |
$x^{12} - 2 x^{11} + 6 x^{10} + 2 x^{9} + 16 x^{8} + 16 x^{6} + 24 x^{4} + 4 x^{3} + 16 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 2\right) x^{4} + 2 t x^{3} + 2 x^{2} + 4 t + 6$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.9 |
$12$ |
$x^{12} - 2 x^{9} + 16 x^{6} - 12 x^{3} + 36$ |
$2$ |
$6$ |
$2$ |
$16$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 6$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.22.54 |
$12$ |
$x^{12} + 8 x^{11} + 28 x^{10} + 44 x^{9} + 24 x^{8} + 68 x^{6} + 24 x^{5} - 36 x^{4} + 72 x^{3} + 8 x^{2} - 16 x + 52$ |
$2$ |
$6$ |
$2$ |
$22$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[3]$ |
$[2, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 8 t + 2$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.75 |
$12$ |
$x^{12} + 8 x^{11} + 28 x^{10} + 44 x^{9} + 24 x^{8} + 92 x^{6} + 120 x^{5} + 108 x^{4} - 24 x^{3} + 56 x^{2} + 80 x + 100$ |
$2$ |
$6$ |
$2$ |
$22$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[3]$ |
$[2, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 6 x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 10$ |
$[6, 0]$ |
$[1, 1]$ |
