| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.1.8.12b1.1 |
$8$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$8$ |
$12$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$2$ |
$t + 1$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 15]$ |
| 2.1.8.12b1.2 |
$8$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$8$ |
$12$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$2$ |
$t + 1$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 15]$ |
| 2.1.8.12b1.3 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$8$ |
$12$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$2$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 10]$ |
| 2.1.8.12b1.4 |
$8$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$8$ |
$12$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$2$ |
$t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 16]$ |
