Defining polynomial
| $x^{3} + b_{8} \pi^{3} x^{2} + b_{7} \pi^{3} x + c_{9} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.5.2.5a1.2 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $8$ |
| Absolute Artin slopes: | $[\frac{5}{2}]$ |
| Swan slopes: | $[3]$ |
| Means: | $\langle2\rangle$ |
| Rams: | $(3)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $59049$ |
| Absolute Mass: | $59049/10$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.