Defining polynomial over unramified subextension
| $x^{9} + 9 b_{16} x^{7} + 3 a_{6} x^{6} + 9 b_{14} x^{5} + 9 a_{13} x^{4} + 9 c_{9} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $105$ |
| Artin slopes: | $[2,\frac{17}{6}]$ |
| Swan slopes: | $[1,\frac{11}{6}]$ |
| Means: | $\langle\frac{2}{3},\frac{13}{9}\rangle$ |
| Rams: | $(1,\frac{7}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $15$ |
| Mass: | $3458145636$ |
| Absolute Mass: | $3458145636/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.