Defining polynomial
| $x^{3} + \left(b_{14} \pi^{5} + b_{11} \pi^{4}\right) x^{2} + \left(b_{13} \pi^{5} + a_{10} \pi^{4}\right) x + c_{15} \pi^{6} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.12.21a1.18 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $12$ |
| Absolute Artin slopes: | $[\frac{9}{4},\frac{9}{4}]$ |
| Swan slopes: | $[5]$ |
| Means: | $\langle\frac{10}{3}\rangle$ |
| Rams: | $(5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $54$ |
| Absolute Mass: | $27$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.