| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.33 |
$12$ |
$x^{12} + 2 x^{10} + 6 x^{9} + 6 x^{8} + 8 x^{7} + 28 x^{6} + 24 x^{5} + 20 x^{4} + 24 x^{3} + 32 x^{2} + 24 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$C_3\times S_4$ (as 12T45) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{2} + 2 x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 2.12.24.142 |
$12$ |
$x^{12} + 16 x^{10} - 52 x^{9} + 18 x^{8} + 64 x^{7} + 144 x^{6} + 144 x^{5} + 108 x^{4} + 64 x^{3} + 288 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_3\times S_4$ (as 12T45) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
| 2.12.24.4 |
$12$ |
$x^{12} - 8 x^{11} + 28 x^{10} + 60 x^{9} + 18 x^{8} + 176 x^{7} + 256 x^{6} + 368 x^{5} + 444 x^{4} + 768 x^{3} + 784 x^{2} + 496 x + 248$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_3\times S_4$ (as 12T45) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(4 t + 4\right) x^{2} + 4 x + 4 t + 6$ |
$[5, 4, 0]$ |
$[1]$ |
