Defining polynomial over unramified subextension
| $x^{6} + 3 a_{1} x + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $30$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $6$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $30$ |
| Artin slopes: | $[\frac{5}{4}]$ |
| Swan slopes: | $[\frac{1}{4}]$ |
| Means: | $\langle\frac{1}{6}\rangle$ |
| Rams: | $(\frac{1}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $10$ |
| Mass: | $242$ |
| Absolute Mass: | $242/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.