Defining polynomial
| $x^{3} + b_{5} \pi^{2} x^{2} + a_{4} \pi^{2} x + c_{6} \pi^{3} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.15.29a1.12 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $6$ |
| Absolute Artin slopes: | $[\frac{7}{5},\frac{5}{2}]$ |
| Swan slopes: | $[2]$ |
| Means: | $\langle\frac{4}{3}\rangle$ |
| Rams: | $(2)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $6$ |
| Absolute Mass: | $6$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.