| Label |
Packet size |
Polynomial |
Galois group |
Galois degree |
$\#\Aut(K/\Q_p)$ |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 5.1.15.15a1.1 |
4 |
$x^{15} + 5 x + 5$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$600$ |
$1$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 4$ |
undefined |
| 5.1.15.15a1.2 |
4 |
$x^{15} + 10 x + 5$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$600$ |
$1$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.15a1.3 |
4 |
$x^{15} + 15 x + 5$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$600$ |
$1$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 2$ |
undefined |
| 5.1.15.15a1.4 |
4 |
$x^{15} + 20 x + 5$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$600$ |
$1$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
