Defining polynomial
| $x^{3} + \left(b_{11} \pi^{4} + a_{8} \pi^{3}\right) x^{2} + b_{10} \pi^{4} x + c_{12} \pi^{5} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.15.29a1.38 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $10$ |
| Absolute Artin slopes: | $[\frac{9}{5},\frac{5}{2}]$ |
| Swan slopes: | $[4]$ |
| Means: | $\langle\frac{8}{3}\rangle$ |
| Rams: | $(4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $18$ |
| Absolute Mass: | $18$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.