Invariants
| Residue field characteristic: | $2$ |
| Degree: | $2$ |
| Base field: | 2.1.10.19a1.32 |
| Ramification index $e$: | $1$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $0$ |
| Absolute Artin slopes: | $[3]$ |
| Swan slopes: | $[\ ]$ |
| Means: | $\langle\ \rangle$ |
| Rams: | $(\ )$ |
| Field count: | $1$ (complete) |
| Ambiguity: | $2$ |
| Mass: | $1$ |
| Absolute Mass: | $1/4$ |
Varying
These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.
| Indices of inseparability: | $[10,0]$ |
| Associated inertia: | $[2,1]$ |
| Jump Set: | $[5,15]$ |
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 |
|---|---|---|---|---|---|---|---|---|
| 2.2.10.38a1.271 | $( x^{2} + x + 1 )^{10} + 4 ( x^{2} + x + 1 )^{9} + 4 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2$ | not computed | $ $not computed$ $ | $4$ | not computed | $[10, 0]$ | $[2, 1]$ | $[5, 15]$ |