Defining polynomial over unramified subextension
| $x^{3} + \left(b_{20} \pi^{7} + b_{17} \pi^{6} + a_{14} \pi^{5}\right) x^{2} + \left(b_{19} \pi^{7} + b_{16} \pi^{6}\right) x + c_{21} \pi^{8} + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.1.6.7a2.1 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $32$ |
| Absolute Artin slopes: | $[\frac{3}{2},\frac{5}{2}]$ |
| Swan slopes: | $[7]$ |
| Means: | $\langle\frac{14}{3}\rangle$ |
| Rams: | $(7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $6$ |
| Mass: | $52488$ |
| Absolute Mass: | $13122$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.