Defining polynomial over unramified subextension
| $x^{3} + b_{11} \pi^{4} x^{2} + \left(b_{13} \pi^{5} + b_{10} \pi^{4}\right) x + \pi$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $6$ |
| Base field: | 3.2.3.6a5.1 |
| Ramification index $e$: | $3$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $22$ |
| Absolute Artin slopes: | $[\frac{3}{2},\frac{17}{6}]$ |
| Swan slopes: | $[\frac{9}{2}]$ |
| Means: | $\langle3\rangle$ |
| Rams: | $(\frac{9}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $531441$ |
| Absolute Mass: | $531441/2$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.