| $x^{2} + a_{1} \pi x + c_{2} \pi^{2} + \pi$ |
These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.
| Galois group: | $C_2^2:Q_8$ |
| Hidden Artin slopes: | $[\ ]^{2}$ |
| Indices of inseparability: | $[35,22,12,12,0]$ |
| Associated inertia: | $[2,1,1]$ |
| Jump Set: | $[1,3,6,12,32]$ |
| 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 |
| 2.1.16.50h1.491 |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 14$ |
$C_2^2:Q_8$ (as 16T31) |
$32$ |
$8$ |
$[2, 2, 3, 4]^{2}$ |
$[1,1,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[35, 22, 12, 12, 0]$ |
$[2, 1, 1]$ |
$z^{12} + 1,z^2 + 1,z + 1$ |
$[1, 3, 6, 12, 32]$ |
Download
displayed columns for
results
