| $x^{2} + a_{1} \pi x + c_{2} \pi^{2} + \pi$ |
These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.
| 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 |
| 2.1.14.14a1.1 |
$x^{14} + 2 x + 2$ |
$F_8:C_6$ (as 14T18) |
$336$ |
$2$ |
$[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]_{7}^{6}$ |
$[\frac{1}{7},\frac{1}{7},\frac{1}{7}]_{7}^{6}$ |
$[\frac{8}{7},\frac{8}{7}]^{6}$ |
$[\frac{1}{7},\frac{1}{7}]^{6}$ |
$[1, 0]$ |
$[3, 1]$ |
$z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ |
$[7, 15]$ |
| 2.1.14.14a1.2 |
$x^{14} + 2 x^{2} + 2 x + 2$ |
$F_8:C_3$ (as 14T11) |
$168$ |
$2$ |
$[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]_{7}^{3}$ |
$[\frac{1}{7},\frac{1}{7},\frac{1}{7}]_{7}^{3}$ |
$[\frac{8}{7},\frac{8}{7}]^{3}$ |
$[\frac{1}{7},\frac{1}{7}]^{3}$ |
$[1, 0]$ |
$[3, 1]$ |
$z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ |
$[7, 15]$ |
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