Defining polynomial
| $x^{3} + \left(b_{26} \pi^{9} + b_{23} \pi^{8} + b_{20} \pi^{7}\right) x^{2} + \left(b_{28} \pi^{10} + b_{25} \pi^{9} + b_{22} \pi^{8} + a_{19} \pi^{7}\right) x + \pi$ |
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 $c$: | $21$ |
| Absolute Artin slopes: | $[2,3,\frac{65}{18}]$ |
| Swan slopes: | $[\frac{19}{2}]$ |
| Means: | $\langle\frac{19}{3}\rangle$ |
| Rams: | $(\frac{19}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $1458$ |
| Absolute Mass: | $162$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.