Defining polynomial over unramified subextension
| $x^{9} + 9 b_{17} x^{8} + 9 a_{16} x^{7} + 9 b_{12} x^{3} + 27 b_{19} x + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $45$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $9$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $120$ |
| Artin slopes: | $[\frac{5}{2},\frac{19}{6}]$ |
| Swan slopes: | $[\frac{3}{2},\frac{13}{6}]$ |
| Means: | $\langle1,\frac{16}{9}\rangle$ |
| Rams: | $(\frac{3}{2},\frac{7}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $5$ |
| Mass: | $3472435494$ |
| Absolute Mass: | $3472435494/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.