Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.12.20.33 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 20 x^{9} + 38 x^{8} + 12 x^{7} + 48 x^{6} + 44 x^{5} + 40 x^{4} - 8 x^{3} + 76 x^{2} - 24 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2^3:S_4$ (as 12T106) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(6 t + 4\right) x^{4} + \left(2 t + 6\right) x^{2} + 4 t x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
2.12.22.12 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 12 x^{9} + 36 x^{8} - 12 x^{7} + 76 x^{6} - 64 x^{5} + 88 x^{4} - 56 x^{3} + 16 x^{2} - 56 x + 196$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2^3:S_4$ (as 12T106) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 t x^{5} + 2 x^{4} + 4 t x^{3} + 4 t x + 14$ |
$[6, 0]$ |
$[1, 1]$ |
2.12.22.25 |
$12$ |
$x^{12} + 8 x^{11} + 12 x^{10} - 16 x^{9} + 16 x^{8} - 4 x^{7} - 12 x^{6} + 48 x^{5} - 8 x^{4} + 16 x^{2} - 8 x + 4$ |
$2$ |
$6$ |
$2$ |
$22$ |
$C_2^3:S_4$ (as 12T106) |
$2$ |
$3$ |
$[3]$ |
$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 4 x^{5} + 4 t x^{4} + 4 t x + 2$ |
$[6, 0]$ |
$[1, 1]$ |