Defining polynomial
| $x^{3} + \left(b_{35} \pi^{12} + b_{32} \pi^{11} + b_{29} \pi^{10} + b_{26} \pi^{9}\right) x^{2} + \left(b_{37} \pi^{13} + b_{34} \pi^{12} + b_{31} \pi^{11} + b_{28} \pi^{10} + a_{25} \pi^{9}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.12.22a1.32 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $27$ |
| Absolute Artin slopes: | $[\frac{19}{8},\frac{71}{24}]$ |
| Swan slopes: | $[\frac{25}{2}]$ |
| Means: | $\langle\frac{25}{3}\rangle$ |
| Rams: | $(\frac{25}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $13122$ |
| Absolute Mass: | $13122$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.