| 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 |
| 3.1.6.11a2.4 |
$6$ |
$x^{6} + 9 x + 6$ |
$3$ |
$1$ |
$6$ |
$11$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t + 1$ |
$x^{6} + 9 x + 6$ |
$[6, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
undefined |
| 3.1.6.11a2.5 |
$6$ |
$x^{6} + 9 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$6$ |
$11$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t + 1$ |
$x^{6} + 9 x^{2} + 9 x + 6$ |
$[6, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
undefined |
| 3.1.6.11a2.6 |
$6$ |
$x^{6} + 18 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$6$ |
$11$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t + 1$ |
$x^{6} + 18 x^{2} + 9 x + 6$ |
$[6, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
undefined |
