Defining polynomial over unramified subextension
| $x^{2} + a_{1} \pi x + c_{2} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $8$ |
| Base field: | 2.1.4.10a1.6 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $8$ |
| Absolute Artin slopes: | $[2,3,\frac{7}{2}]$ |
| Swan slopes: | $[1]$ |
| Means: | $\langle\frac{1}{2}\rangle$ |
| Rams: | $(1)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $15$ |
| Absolute Mass: | $15/8$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.