Defining polynomial over unramified subextension
| $x^{2} + \left(b_{9} \pi^{5} + b_{7} \pi^{4} + a_{5} \pi^{3}\right) x + c_{10} \pi^{6} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.22d1.17 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $12$ |
| Absolute Artin slopes: | $[2,3,\frac{7}{2},\frac{7}{2}]$ |
| Swan slopes: | $[5]$ |
| Means: | $\langle\frac{5}{2}\rangle$ |
| Rams: | $(5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $48$ |
| Absolute Mass: | $3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.