Defining polynomial
| $x^{3} + \left(b_{44} \pi^{15} + b_{41} \pi^{14} + b_{38} \pi^{13} + b_{35} \pi^{12} + b_{32} \pi^{11}\right) x^{2} + \left(b_{46} \pi^{16} + b_{43} \pi^{15} + b_{40} \pi^{14} + b_{37} \pi^{13} + b_{34} \pi^{12} + a_{31} \pi^{11}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.12.21a2.23 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $33$ |
| Absolute Artin slopes: | $[\frac{9}{4},\frac{25}{8}]$ |
| Swan slopes: | $[\frac{31}{2}]$ |
| Means: | $\langle\frac{31}{3}\rangle$ |
| Rams: | $(\frac{31}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $118098$ |
| Absolute Mass: | $39366$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.