Defining polynomial over unramified subextension
| $x^{2} + \left(b_{17} \pi^{9} + b_{15} \pi^{8} + b_{13} \pi^{7} + b_{11} \pi^{6} + a_{9} \pi^{5}\right) x + c_{18} \pi^{10} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.12b1.1 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $20$ |
| Absolute Artin slopes: | $[\frac{4}{3},\frac{4}{3},2,\frac{11}{4}]$ |
| Swan slopes: | $[9]$ |
| Means: | $\langle\frac{9}{2}\rangle$ |
| Rams: | $(9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $768$ |
| Absolute Mass: | $192$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.