Defining polynomial over unramified subextension
| $x^{5} + a_{4} \pi x^{4} + c_{5} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $5$ |
| Degree: | $10$ |
| Base field: | 5.1.4.3a1.2 |
| Ramification index $e$: | $5$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $16$ |
| Absolute Artin slopes: | $[\frac{5}{4}]$ |
| Swan slopes: | $[1]$ |
| Means: | $\langle\frac{4}{5}\rangle$ |
| Rams: | $(1)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $10$ |
| Mass: | $24$ |
| Absolute Mass: | $3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.