Defining polynomial over unramified subextension
| $x^{4} + \left(b_{11} \pi^{3} + a_{7} \pi^{2}\right) x^{3} + a_{2} \pi x^{2} + b_{9} \pi^{3} x + c_{12} \pi^{4} + c_{4} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $20$ |
| Base field: | $\Q_{2}(\sqrt{-2\cdot 5})$ |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $50$ |
| Absolute Artin slopes: | $[2,3,\frac{7}{2}]$ |
| Swan slopes: | $[1,3]$ |
| Means: | $\langle\frac{1}{2},\frac{7}{4}\rangle$ |
| Rams: | $(1,5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $20$ |
| Mass: | $984064$ |
| Absolute Mass: | $492032/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.