| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.16.20 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{7} + 2 x^{6} + 4 x^{5} + 4 x^{4} - 4 x^{3} - 4 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.6 |
$12$ |
$x^{12} - 2 x^{9} - 2 x^{6} + 24 x^{3} + 36$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 6 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.7 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 12 x^{9} + 8 x^{8} + 4 x^{7} + 6 x^{6} + 20 x^{5} + 20 x^{4} + 4 x^{3} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t + 2\right) x^{4} + 2 x^{3} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.8 |
$12$ |
$x^{12} + 2 x^{11} + 4 x^{10} - 2 x^{9} + 6 x^{8} + 8 x^{7} + 6 x^{6} + 24 x^{5} + 4 x^{4} + 16 x^{3} + 20 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.22.11 |
$12$ |
$x^{12} + 8 x^{10} + 32 x^{8} + 4 x^{7} + 2 x^{6} + 40 x^{5} + 32 x^{4} + 8 x^{3} - 12 x^{2} + 56 x + 196$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[3]$ |
$[2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 14 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.71 |
$12$ |
$x^{12} + 8 x^{10} + 4 x^{9} + 32 x^{8} + 44 x^{7} + 18 x^{6} + 48 x^{5} + 64 x^{4} + 64 x^{3} - 12 x^{2} + 56 x + 196$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[3]$ |
$[2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + \left(4 t + 4\right) x + 14 t$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.77 |
$12$ |
$x^{12} + 8 x^{10} + 32 x^{8} + 4 x^{7} + 18 x^{6} + 40 x^{5} + 96 x^{4} + 8 x^{3} + 20 x^{2} + 88 x + 148$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[3]$ |
$[2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 14 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.78 |
$12$ |
$x^{12} + 8 x^{10} + 4 x^{9} + 32 x^{8} + 44 x^{7} + 34 x^{6} + 48 x^{5} + 128 x^{4} + 96 x^{3} + 20 x^{2} + 88 x + 148$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[3]$ |
$[2, 3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(4 t + 6\right) x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + \left(4 t + 4\right) x + 14 t + 8$ |
$[6, 0]$ |
$[1, 1]$ |
