| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.6.6.6 |
$6$ |
$x^{6} + 3 x + 3$ |
$3$ |
$6$ |
$1$ |
$6$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.6.6.7 |
$6$ |
$x^{6} + 3 x + 6$ |
$3$ |
$6$ |
$1$ |
$6$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x + 6$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.6.10.10 |
$6$ |
$x^{6} + 3 x^{5} + 18 x^{2} + 18 x + 15$ |
$3$ |
$6$ |
$1$ |
$10$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 18 x^{2} + 18 x + 15$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.6.10.11 |
$6$ |
$x^{6} + 3 x^{5} + 9 x^{2} + 9 x + 24$ |
$3$ |
$6$ |
$1$ |
$10$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 9 x^{2} + 9 x + 24$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.6.10.12 |
$6$ |
$x^{6} + 3 x^{5} + 3$ |
$3$ |
$6$ |
$1$ |
$10$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 3$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.6.10.7 |
$6$ |
$x^{6} + 3 x^{5} + 6$ |
$3$ |
$6$ |
$1$ |
$10$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.6.10.8 |
$6$ |
$x^{6} + 3 x^{5} + 18 x^{2} + 18 x + 21$ |
$3$ |
$6$ |
$1$ |
$10$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 18 x^{2} + 18 x + 21$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.6.10.9 |
$6$ |
$x^{6} + 3 x^{5} + 9 x^{2} + 9 x + 12$ |
$3$ |
$6$ |
$1$ |
$10$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{6} + 3 x^{5} + 9 x^{2} + 9 x + 12$ |
$[5, 0]$ |
$[1, 1]$ |
