| 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 |
| 2.2.8.40c1.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2\wr S_3$ (as 16T765) |
$2$ |
$3$ |
$[\frac{8}{3}, \frac{8}{3}, 3]$ |
$[\frac{5}{3},\frac{5}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3},2]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3},2]_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 t x^{4} + 4 x^{2} + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40c1.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2\wr S_3$ (as 16T765) |
$2$ |
$3$ |
$[\frac{8}{3}, \frac{8}{3}, 3]$ |
$[\frac{5}{3},\frac{5}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3},2]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3},2]_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 t x^{4} + 4 x^{2} + 8 t + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40c1.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2\wr S_3$ (as 16T765) |
$2$ |
$3$ |
$[\frac{8}{3}, \frac{8}{3}, 3]$ |
$[\frac{5}{3},\frac{5}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3},2]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3},2]_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{5} + 4 t x^{4} + 4 x^{2} + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40c1.12 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2\wr S_3$ (as 16T765) |
$2$ |
$3$ |
$[\frac{8}{3}, \frac{8}{3}, 3]$ |
$[\frac{5}{3},\frac{5}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3},2]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3},2]_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{5} + 4 t x^{4} + 4 x^{2} + 8 t + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
