Defining polynomial over unramified subextension
| $x^{5} + 5 a_{4} x^{4} + 25 c_{5} + 5$ |
Invariants
| Residue field characteristic: | $5$ |
| Degree: | $25$ |
| Base field: | $\Q_{5}$ |
| Ramification index $e$: | $5$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $40$ |
| Artin slopes: | $[2]$ |
| Swan slopes: | $[1]$ |
| Means: | $\langle\frac{4}{5}\rangle$ |
| Rams: | $(1)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $25$ |
| Mass: | $3124$ |
| Absolute Mass: | $3124/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.