Defining polynomial
| $x^{25} + 5 b_{22} x^{22} + 5 a_{21} x^{21} + 5 a_{15} x^{15} + 5$ |
Invariants
| Residue field characteristic: | $5$ |
| Degree: | $25$ |
| Base field: | $\Q_{5}$ |
| Ramification index $e$: | $25$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $45$ |
| Artin slopes: | $[\frac{7}{4},\frac{19}{10}]$ |
| Swan slopes: | $[\frac{3}{4},\frac{9}{10}]$ |
| Means: | $\langle\frac{3}{5},\frac{21}{25}\rangle$ |
| Rams: | $(\frac{3}{4},\frac{3}{2})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $80$ |
| Absolute Mass: | $80$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.