Defining polynomial over unramified subextension
| $x^{15} + 3 c_{12} x^{12} + 3 b_{11} x^{11} + 3 b_{10} x^{10} + 3 a_{8} x^{8} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $15$ |
| Residue field degree $f$: | $3$ |
| Discriminant exponent $c$: | $66$ |
| Artin slopes: | $[\frac{9}{5}]$ |
| Swan slopes: | $[\frac{4}{5}]$ |
| Means: | $\langle\frac{8}{15}\rangle$ |
| Rams: | $(4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $9$ |
| Mass: | $18954$ |
| Absolute Mass: | $6318$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.