Defining polynomial over unramified subextension
| $x^{9} + 27 b_{22} x^{4} + 9 b_{12} x^{3} + 27 b_{20} x^{2} + 27 b_{19} x + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $36$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $104$ |
| Artin slopes: | $[\frac{5}{2},\frac{7}{2}]$ |
| Swan slopes: | $[\frac{3}{2},\frac{5}{2}]$ |
| Means: | $\langle1,2\rangle$ |
| Rams: | $(\frac{3}{2},\frac{9}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $43046721$ |
| Absolute Mass: | $43046721/4$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.