Defining polynomial
| $x^{3} + \left(b_{53} \pi^{18} + b_{50} \pi^{17} + b_{47} \pi^{16} + b_{44} \pi^{15} + b_{41} \pi^{14} + b_{38} \pi^{13}\right) x^{2} + \left(b_{52} \pi^{18} + b_{49} \pi^{17} + b_{46} \pi^{16} + b_{43} \pi^{15} + b_{40} \pi^{14} + b_{37} \pi^{13}\right) x + c_{54} \pi^{19} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $3$ |
| Base field: | 3.1.12.21a2.25 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $38$ |
| Absolute Artin slopes: | $[\frac{9}{4},\frac{10}{3}]$ |
| Swan slopes: | $[18]$ |
| Means: | $\langle12\rangle$ |
| Rams: | $(18)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $3$ |
| Mass: | $531441$ |
| Absolute Mass: | $177147$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.