| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.20.21 |
$12$ |
$x^{12} - 2 x^{11} + 2 x^{10} + 16 x^{9} + 8 x^{8} - 20 x^{7} + 12 x^{6} + 52 x^{5} + 40 x^{4} + 32 x^{3} + 48 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{4} + 4 x^{3} + 6 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.25 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 16 x^{9} + 28 x^{8} - 4 x^{7} + 24 x^{6} + 24 x^{5} + 68 x^{4} + 24 x^{3} + 40 x^{2} + 8 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 2\right) x^{2} + 4 t x + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.31 |
$12$ |
$x^{12} - 2 x^{11} + 10 x^{10} - 4 x^{9} + 32 x^{8} - 4 x^{7} + 36 x^{6} - 4 x^{5} + 40 x^{4} + 8 x^{3} + 16 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 4\right) x^{4} + 4 t x^{3} + 2 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.7 |
$12$ |
$x^{12} - 2 x^{11} + 10 x^{10} + 8 x^{9} + 16 x^{8} + 12 x^{7} + 60 x^{6} + 52 x^{5} + 72 x^{4} + 32 x^{3} + 48 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 4\right) x^{4} + 4 x^{3} + 6 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.22.1 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 8 x^{9} + 16 x^{8} - 28 x^{7} + 56 x^{6} + 64 x^{5} + 36 x^{4} - 24 x^{3} + 16 x^{2} + 72 x + 108$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 6 x^{2} + 4 t x + 12 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.3 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 8 x^{9} + 16 x^{8} - 28 x^{7} + 64 x^{6} + 52 x^{4} - 24 x^{3} + 64 x^{2} + 8 x + 28$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 6 x^{2} + 4 t x + 4 t + 6$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.44 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{10} - 16 x^{9} + 14 x^{8} + 92 x^{7} + 4 x^{6} + 40 x^{5} - 28 x^{4} + 16 x^{3} + 148 x^{2} + 88 x + 124$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 6 x^{4} + 4 x^{3} + 6 t x^{2} + 4 t x + 12 t + 2$ |
$[6, 0]$ |
$[1, 1]$ |
| 2.12.22.48 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{10} - 16 x^{9} + 14 x^{8} + 92 x^{7} + 28 x^{6} - 56 x^{5} + 116 x^{4} + 112 x^{3} + 4 x^{2} - 8 x + 76$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 2, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 6 x^{4} + 4 x^{3} + 6 t x^{2} + 4 t x + 4 t + 10$ |
$[6, 0]$ |
$[1, 1]$ |
