Defining polynomial
| $x^{3} + \left(b_{38} \pi^{13} + b_{35} \pi^{12} + b_{32} \pi^{11} + b_{29} \pi^{10}\right) x^{2} + \left(b_{40} \pi^{14} + b_{37} \pi^{13} + b_{34} \pi^{12} + b_{31} \pi^{11} + b_{28} \pi^{10}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.9.22a3.8 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $29$ |
| Absolute Artin slopes: | $[2,3,\frac{73}{18}]$ |
| Swan slopes: | $[\frac{27}{2}]$ |
| Means: | $\langle9\rangle$ |
| Rams: | $(\frac{27}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $19683$ |
| Absolute Mass: | $2187$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.