Defining polynomial over unramified subextension
| $x^{9} + 3a_{5} x^{5} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $27$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $3$ |
| Discriminant exponent $c$: | $39$ |
| Artin slopes: | $[\frac{13}{8},\frac{13}{8}]$ |
| Swan slopes: | $[\frac{5}{8},\frac{5}{8}]$ |
| Means: | $\langle\frac{5}{12},\frac{5}{9}\rangle$ |
| Rams: | $(\frac{5}{8},\frac{5}{8})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $26$ |
| Absolute Mass: | $26/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.