Defining polynomial over unramified subextension
| $x^{9} + 3 a_{6} x^{6} + 9 c_{12} x^{3} + 9 b_{11} x^{2} + 9 a_{10} x + 9 c_{9} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $90$ |
| Artin slopes: | $[2,\frac{7}{3}]$ |
| Swan slopes: | $[1,\frac{4}{3}]$ |
| Means: | $\langle\frac{2}{3},\frac{10}{9}\rangle$ |
| Rams: | $(1,2)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $45$ |
| Mass: | $14231052$ |
| Absolute Mass: | $14231052/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.