| 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 |
| 3.1.12.22a1.7 |
$12$ |
$x^{12} + 3 x^{11} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$22$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[\frac{19}{8}]$ |
$[\frac{11}{8}]$ |
$[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ |
$[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ |
$[\frac{19}{8}]^{2}_{2}$ |
$[\frac{11}{8}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 18 x^{2} + 3$ |
$[11, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z + 1$ |
$[2, 14]$ |
| 3.1.12.22a1.8 |
$12$ |
$x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$22$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[\frac{19}{8}]$ |
$[\frac{11}{8}]$ |
$[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ |
$[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ |
$[\frac{19}{8}]^{2}_{2}$ |
$[\frac{11}{8}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 3$ |
$[11, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z + 1$ |
$[2, 14]$ |
| 3.1.12.22a1.9 |
$12$ |
$x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$22$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[\frac{19}{8}]$ |
$[\frac{11}{8}]$ |
$[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ |
$[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ |
$[\frac{19}{8}]^{2}_{2}$ |
$[\frac{11}{8}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 3$ |
$[11, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z + 1$ |
$[2, 14]$ |
| 3.1.12.22a1.31 |
$12$ |
$x^{12} + 3 x^{11} + 9 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$22$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[\frac{19}{8}]$ |
$[\frac{11}{8}]$ |
$[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ |
$[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ |
$[\frac{19}{8}]^{2}_{2}$ |
$[\frac{11}{8}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 9 x^{2} + 6$ |
$[11, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z + 2$ |
undefined |
| 3.1.12.22a1.32 |
$12$ |
$x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$22$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[\frac{19}{8}]$ |
$[\frac{11}{8}]$ |
$[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ |
$[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ |
$[\frac{19}{8}]^{2}_{2}$ |
$[\frac{11}{8}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 6$ |
$[11, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z + 2$ |
undefined |
| 3.1.12.22a1.33 |
$12$ |
$x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$22$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[\frac{19}{8}]$ |
$[\frac{11}{8}]$ |
$[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ |
$[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ |
$[\frac{19}{8}]^{2}_{2}$ |
$[\frac{11}{8}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 6$ |
$[11, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z + 2$ |
undefined |
