Defining polynomial
| $x^{30} + 3 b_{10} x^{10} + 3 b_{8} x^{8} + 3 a_{7} x^{7} + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $30$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $30$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $36$ |
| Artin slopes: | $[\frac{27}{20}]$ |
| Swan slopes: | $[\frac{7}{20}]$ |
| Means: | $\langle\frac{7}{30}\rangle$ |
| Rams: | $(\frac{7}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $18$ |
| Absolute Mass: | $18$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.