| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.30 |
$12$ |
$x^{12} + 4 x^{8} + 2 x^{7} - 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 4$ |
$2$ |
$6$ |
$2$ |
$12$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{2} + \left(2 t + 2\right) x + 2 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 2.12.20.4 |
$12$ |
$x^{12} + 2 x^{11} + 8 x^{10} + 16 x^{9} + 20 x^{8} + 8 x^{7} + 26 x^{6} + 52 x^{5} + 44 x^{4} + 8 x^{3} + 20 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(4 t + 4\right) x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.48 |
$12$ |
$x^{12} - 2 x^{11} + 12 x^{10} + 8 x^{9} + 36 x^{8} + 40 x^{7} + 18 x^{6} + 16 x^{5} + 44 x^{4} + 40 x^{3} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 4\right) x^{3} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.50 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{9} + 24 x^{8} + 36 x^{7} + 50 x^{6} + 36 x^{5} + 72 x^{4} + 64 x^{3} + 28 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.6 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 16 x^{8} + 28 x^{7} + 34 x^{6} + 12 x^{5} + 40 x^{4} + 24 x^{3} + 28 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 6 x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
