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 |
3.2.6.22a1.3 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 9\right) x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.7 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 18\right) x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.11 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(9 t + 18\right) x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
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