Defining polynomial
| $x^{3} + a_{5} \pi^{2} x^{2} + b_{7} \pi^{3} x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.15.29a1.32 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $7$ |
| Absolute Artin slopes: | $[\frac{3}{2},\frac{5}{2}]$ |
| Swan slopes: | $[\frac{5}{2}]$ |
| Means: | $\langle\frac{5}{3}\rangle$ |
| Rams: | $(\frac{5}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $6$ |
| Absolute Mass: | $6$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.