| $x^{4} + a_{1} \pi x + \pi$ |
These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.
| Galois group: | $C_4\times S_4$ |
| Hidden Artin slopes: | $[\ ]^{2}_{3}$ |
| Indices of inseparability: | $[33,18,4,4,0]$ |
| Associated inertia: | $[1,1,1]$ |
| Jump Set: | $[1,2,5,13,29]$ |
| Label |
Polynomial $/ \Q_p$ |
Galois group $/ \Q_p$ |
Galois degree $/ \Q_p$ |
$\#\Aut(K/\Q_p)$ |
Artin slope content $/ \Q_p$ |
Swan slope content $/ \Q_p$ |
Hidden Artin slopes $/ \Q_p$ |
Hidden Swan slopes $/ \Q_p$ |
Ind. of Insep. $/ \Q_p$ |
Assoc. Inertia $/ \Q_p$ |
Resid. Poly |
Jump Set |
| 2.1.16.48h1.972 |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 18$ |
$C_4\times S_4$ (as 16T181) |
$96$ |
$4$ |
$[\frac{4}{3}, \frac{4}{3}, 3, 4]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},2,3]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$[33, 18, 4, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 5, 13, 29]$ |
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