Defining polynomial over unramified subextension
| $x^{2} + \left(b_{13} \pi^{7} + b_{11} \pi^{6} + b_{9} \pi^{5} + a_{7} \pi^{4}\right) x + c_{14} \pi^{8} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.2.4.22a1.1 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $16$ |
| Absolute Artin slopes: | $[3,4,\frac{19}{4}]$ |
| Swan slopes: | $[7]$ |
| Means: | $\langle\frac{7}{2}\rangle$ |
| Rams: | $(7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $61440$ |
| Absolute Mass: | $7680$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.