| 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 |
| 3.2.6.22a1.40 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.41 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.42 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.46 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.47 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.48 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 9 x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.52 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.53 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + 18 x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
| 3.2.6.22a1.54 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{2}$ |
$[1,\frac{3}{2}]_{2}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 18 x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
