Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.2.3.6a5.1 |
| Ramification index $e$: | $1$ |
| Residue field degree $f$: | $3$ |
| Discriminant exponent $c$: | $0$ |
| Absolute Artin slopes: | $[\frac{3}{2}]$ |
| 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 $\Q_{ 3 }$ within this relative family, not the relative extension.
| Indices of inseparability: | $[1,0]$ |
| Associated inertia: | $[1]$ |
| 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 |
|---|---|---|---|---|---|---|---|---|
| 3.6.3.18a47.1 | $( x^{6} + 2 x^{4} + x^{2} + 2 x + 2 )^{3} + \left(6 x^{5} + 6 x^{3} + 3 x^{2} + 6 x + 6\right) ( x^{6} + 2 x^{4} + x^{2} + 2 x + 2 ) + 3$ | $C_3^2:C_{12}$ (as 18T44) | $108$ | $3$ | not computed | $[1, 0]$ | $[1]$ | undefined |