Defining polynomial
| $x^{30} + 3 a_{29} x^{29} + 9 b_{43} x^{13} + 9 b_{41} x^{11} + 9 b_{40} x^{10} + 9 b_{38} x^{8} + 9 b_{37} x^{7} + 9 b_{35} x^{5} + 9 b_{34} x^{4} + 9 b_{32} x^{2} + 9 b_{31} x + 3 d_{0}$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $30$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $30$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $58$ |
| Artin slopes: | $[\frac{49}{20}]$ |
| Swan slopes: | $[\frac{29}{20}]$ |
| Means: | $\langle\frac{29}{30}\rangle$ |
| Rams: | $(\frac{29}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $39366$ |
| Absolute Mass: | $39366$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.