Defining polynomial over unramified subextension
| $x^{3} + 3 a_{2} x^{2} + 9 c_{3} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $30$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $10$ |
| Discriminant exponent $c$: | $40$ |
| Artin slopes: | $[2]$ |
| Swan slopes: | $[1]$ |
| Means: | $\langle\frac{2}{3}\rangle$ |
| Rams: | $(1)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $30$ |
| Mass: | $59048$ |
| Absolute Mass: | $29524/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.