Defining polynomial
| $x^{3} + \left(b_{14} \pi^{5} + a_{11} \pi^{4}\right) x^{2} + \left(b_{16} \pi^{6} + b_{13} \pi^{5}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.12.21a2.31 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $13$ |
| Absolute Artin slopes: | $[\frac{9}{4},\frac{55}{24}]$ |
| Swan slopes: | $[\frac{11}{2}]$ |
| Means: | $\langle\frac{11}{3}\rangle$ |
| Rams: | $(\frac{11}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $54$ |
| Absolute Mass: | $18$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.