Invariants
| Residue field characteristic: | $19$ |
| Degree: | $3$ |
| Base field: | 19.6.1.0a1.1 |
| Ramification index $e$: | $1$ |
| Residue field degree $f$: | $3$ |
| Discriminant exponent $c$: | $0$ |
| Absolute Artin slopes: | $[\ ]$ |
| Swan slopes: | $[\ ]$ |
| Means: | $\langle\ \rangle$ |
| Rams: | $(\ )$ |
| Field count: | $1$ (complete) |
| Ambiguity: | $3$ |
| Mass: | $1$ |
| Absolute Mass: | $1/18$ |
Varying
These invariants are all associated to absolute extensions of $\Q_{ 19 }$ within this relative family, not the relative extension.
| Galois group: | $C_{18}$ |
| Hidden Artin slopes: | $[\ ]$ |
| Indices of inseparability: | $[0]$ |
| Associated inertia: | $[\ ]$ |
| 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 |
|---|---|---|---|---|---|---|---|---|
| 19.18.1.0a1.1 | $x^{18} + 10 x^{11} + 9 x^{10} + 7 x^{9} + 17 x^{8} + 5 x^{7} + 16 x^{5} + 5 x^{4} + 7 x^{3} + 3 x^{2} + 14 x + 2$ | $C_{18}$ (as 18T1) | $18$ | $18$ | $[\ ]$ | $[0]$ | $[\ ]$ | undefined |