Defining polynomial
| $x^{2} + d_{0} \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $2$ |
| Base field: | 3.1.9.9a1.1 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $1$ |
| Absolute Artin slopes: | $[\frac{9}{8},\frac{9}{8}]$ |
| Swan slopes: | $[\ ]$ |
| Means: | $\langle\ \rangle$ |
| Rams: | $(\ )$ |
| Field count: | $2$ (complete) |
| Ambiguity: | $2$ |
| Mass: | $1$ |
| Absolute Mass: | $1$ |
Varying
These invariants are all associated to absolute extensions of $\Q_{ 3 }$ within this relative family, not the relative extension.
| Indices of inseparability: | $[2,2,0]$ |
| Associated inertia: | $[1,1]$ (show 1), $[1,2]$ (show 1) |
| Jump Set: | undefined (show 1), $[1,3,11]$ (show 1) |
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 |
|---|---|---|---|---|---|---|---|---|
| 3.1.18.19a1.1 | $x^{18} + 3 x^{2} + 3$ | $F_9:C_2$ (as 18T73) | $144$ | $2$ | not computed | $[2, 2, 0]$ | $[1, 1]$ | $[1, 3, 11]$ |