Defining polynomial over unramified subextension
| $x^{2} + \left(b_{7} \pi^{4} + b_{5} \pi^{3}\right) x + c_{8} \pi^{5} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $10$ |
| Base field: | 2.2.2.6a1.4 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $25$ |
| Absolute Artin slopes: | $[3,4]$ |
| Swan slopes: | $[4]$ |
| Means: | $\langle2\rangle$ |
| Rams: | $(4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $10$ |
| Mass: | $1048576$ |
| Absolute Mass: | $524288/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.