Defining polynomial
| $x^{4} + d_{0} \pi$ |
Invariants
| Residue field characteristic: | $197$ |
| Degree: | $4$ |
| Base field: | 197.1.4.3a1.2 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $3$ |
| Absolute Artin slopes: | $[\ ]$ |
| Swan slopes: | $[\ ]$ |
| Means: | $\langle\ \rangle$ |
| Rams: | $(\ )$ |
| Field count: | $1$ (complete) |
| Ambiguity: | $4$ |
| Mass: | $1$ |
| Absolute Mass: | $1/4$ |
Varying
These invariants are all associated to absolute extensions of $\Q_{ 197 }$ within this relative family, not the relative extension.
| Galois group: | $C_{16}:C_4$ |
| Hidden Artin slopes: | $[\ ]^{4}$ |
| Indices of inseparability: | $[0]$ |
| Associated inertia: | $[4]$ |
| 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 |
|---|---|---|---|---|---|---|---|---|
| 197.1.16.15a1.2 | $x^{16} + 394$ | $C_{16}:C_4$ (as 16T125) | $64$ | $4$ | $[\ ]^{4}$ | $[0]$ | $[4]$ | undefined |