Defining polynomial
| $x^{25} + 5 a_{10} x^{10} + 25 b_{31} x^{6} + 25 b_{29} x^{4} + 25 b_{28} x^{3} + 25 a_{27} x^{2} + 5$ |
Invariants
| Residue field characteristic: | $5$ |
| Degree: | $25$ |
| Base field: | $\Q_{5}$ |
| Ramification index $e$: | $25$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $51$ |
| Artin slopes: | $[\frac{3}{2},\frac{9}{4}]$ |
| Swan slopes: | $[\frac{1}{2},\frac{5}{4}]$ |
| Means: | $\langle\frac{2}{5},\frac{27}{25}\rangle$ |
| Rams: | $(\frac{1}{2},\frac{17}{4})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $1$ |
| Mass: | $2000$ |
| Absolute Mass: | $2000$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.