Defining polynomial over unramified subextension
| $x^{9} + 3 a_{8} x^{8} + 3 a_{3} x^{3} + 9 b_{10} x + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $64$ |
| Artin slopes: | $[\frac{3}{2},\frac{13}{6}]$ |
| Swan slopes: | $[\frac{1}{2},\frac{7}{6}]$ |
| Means: | $\langle\frac{1}{3},\frac{8}{9}\rangle$ |
| Rams: | $(\frac{1}{2},\frac{5}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $518400$ |
| Absolute Mass: | $129600$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.