Invariants
| Residue field characteristic: | $191$ |
| Degree: | $4$ |
| Base field: | $\Q_{191}(\sqrt{7})$ |
| Ramification index $e$: | $1$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $0$ |
| Absolute Artin slopes: | $[\ ]$ |
| Swan slopes: | $[\ ]$ |
| Means: | $\langle\ \rangle$ |
| Rams: | $(\ )$ |
| Field count: | $1$ (complete) |
| Ambiguity: | $4$ |
| Mass: | $1$ |
| Absolute Mass: | $1/8$ |
Varying
These invariants are all associated to absolute extensions of $\Q_{ 191 }$ within this relative family, not the relative extension.
| Galois group: | $C_8$ |
| Hidden Artin slopes: | $[\ ]$ |
| Indices of inseparability: | $[0]$ |
| Associated inertia: | $[\ ]$ |
| Jump Set: | undefined |
Fields
Showing all 1
Download displayed columns for results| Label | Polynomial $/ \Q_p$ | Galois group $/ \Q_p$ | Galois degree $/ \Q_p$ | $\#\Aut(K/\Q_p)$ | Hidden Artin slopes $/ \Q_p$ | Ind. of Insep. $/ \Q_p$ | Assoc. Inertia $/ \Q_p$ | Jump Set |
|---|---|---|---|---|---|---|---|---|
| 191.8.1.0a1.1 | $x^{8} + 2 x^{4} + 164 x^{3} + 139 x^{2} + 171 x + 19$ | $C_8$ (as 8T1) | $8$ | $8$ | $[\ ]$ | $[0]$ | $[\ ]$ | undefined |