Defining polynomial
| $x^{3} + \left(b_{59} \pi^{20} + b_{56} \pi^{19} + b_{53} \pi^{18} + b_{50} \pi^{17} + b_{47} \pi^{16} + b_{44} \pi^{15} + b_{41} \pi^{14}\right) x^{2} + \left(b_{58} \pi^{20} + b_{55} \pi^{19} + b_{52} \pi^{18} + b_{49} \pi^{17} + b_{46} \pi^{16} + b_{43} \pi^{15} + a_{40} \pi^{14}\right) x + c_{60} \pi^{21} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.15.29a1.31 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $42$ |
| Absolute Artin slopes: | $[\frac{5}{2},\frac{10}{3}]$ |
| Swan slopes: | $[20]$ |
| Means: | $\langle\frac{40}{3}\rangle$ |
| Rams: | $(20)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $3188646$ |
| Absolute Mass: | $3188646$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.