Defining polynomial
| $x^{30} + 3 b_{29} x^{29} + 3 b_{28} x^{28} + 3 b_{26} x^{26} + 3 a_{25} x^{25} + 9 b_{37} x^{7} + 9 b_{35} x^{5} + 9 b_{34} x^{4} + 9 b_{32} x^{2} + 9 b_{31} x + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $30$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $30$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $54$ |
| Artin slopes: | $[\frac{9}{4}]$ |
| Swan slopes: | $[\frac{5}{4}]$ |
| Means: | $\langle\frac{5}{6}\rangle$ |
| Rams: | $(\frac{25}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $13122$ |
| Absolute Mass: | $13122$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.