Defining polynomial over unramified subextension
| $x^{3} + a_{1} \pi x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.1.6.7a1.4 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $6$ |
| Absolute Artin slopes: | $[\frac{5}{4},\frac{3}{2}]$ |
| Swan slopes: | $[\frac{1}{2}]$ |
| Means: | $\langle\frac{1}{3}\rangle$ |
| Rams: | $(\frac{1}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $8$ |
| Absolute Mass: | $4/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.