Defining polynomial
| $x^{3} + d_{0} \pi$ |
Invariants
| Residue field characteristic: | $7$ |
| Degree: | $3$ |
| Base field: | 7.1.3.2a1.1 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $2$ |
| Absolute Artin slopes: | $[\ ]$ |
| Swan slopes: | $[\ ]$ |
| Means: | $\langle\ \rangle$ |
| Rams: | $(\ )$ |
| Field count: | $1$ (complete) |
| Ambiguity: | $3$ |
| Mass: | $1$ |
| Absolute Mass: | $1/3$ |
Varying
These invariants are all associated to absolute extensions of $\Q_{ 7 }$ within this relative family, not the relative extension.
| Galois group: | $C_9:C_3$ |
| Hidden Artin slopes: | $[\ ]^{3}$ |
| Indices of inseparability: | $[0]$ |
| Associated inertia: | $[3]$ |
| 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 |
|---|---|---|---|---|---|---|---|---|
| 7.1.9.8a1.1 | $x^{9} + 7$ | $C_9:C_3$ (as 9T6) | $27$ | $3$ | $[\ ]^{3}$ | $[0]$ | $[3]$ | undefined |