Defining polynomial over unramified subextension
| $x^{3} + \left(b_{14} \pi^{5} + a_{11} \pi^{4}\right) x^{2} + \left(b_{16} \pi^{6} + b_{13} \pi^{5}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.1.6.11a1.7 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $26$ |
| Absolute Artin slopes: | $[\frac{5}{2},\frac{35}{12}]$ |
| Swan slopes: | $[\frac{11}{2}]$ |
| Means: | $\langle\frac{11}{3}\rangle$ |
| Rams: | $(\frac{11}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $5832$ |
| Absolute Mass: | $972$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.