| $x^{6} + b_{5} \pi x^{5} + a_{3} \pi x^{3} + c_{6} \pi^{2} + \pi$ |
These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.
| 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 |
| 2.1.12.20a1.1 |
$x^{12} + 2 x^{9} + 2$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$24$ |
$2$ |
$[2, 2]_{3}^{2}$ |
$[1,1]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 18]$ |
| 2.1.12.20a1.7 |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T52) |
$96$ |
$2$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 18]$ |
Download
displayed columns for
results
