| 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 |
| 3.1.12.13a1.1 |
$12$ |
$x^{12} + 3 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$13$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]^{2}$ |
$[\frac{1}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 8]$ |
| 3.1.12.13a1.2 |
$12$ |
$x^{12} + 6 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$13$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]^{2}$ |
$[\frac{1}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 6 x^{2} + 6$ |
$[2, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.1 |
$12$ |
$x^{12} + 6 x^{10} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.2 |
$12$ |
$x^{12} + 6 x^{10} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.3 |
$12$ |
$x^{12} + 6 x^{10} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 18 x^{2} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.16 |
$12$ |
$x^{12} + 3 x^{10} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.17 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.18 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
