Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.12.13.1 |
$12$ |
$x^{12} + 3 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[2, 2]$ |
3.12.13.2 |
$12$ |
$x^{12} + 3 x^{3} + 6 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$13$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
3.12.13.3 |
$12$ |
$x^{12} + 3 x^{3} + 3 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$13$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{3} + 3 x^{2} + 6$ |
$[2, 0]$ |
$[1, 2]$ |
3.12.13.4 |
$12$ |
$x^{12} + 6 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{2} + 6$ |
$[2, 0]$ |
$[2, 2]$ |
3.12.13.5 |
$12$ |
$x^{12} + 6 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
3.12.13.6 |
$12$ |
$x^{12} + 3 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{2} + 6$ |
$[2, 0]$ |
$[1, 2]$ |