Defining polynomial over unramified subextension
| $x^{2} + \left(b_{5} \pi^{3} + a_{3} \pi^{2}\right) x + c_{6} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.12b1.3 |
| Ramification index $e$: | $2$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $8$ |
| Absolute Artin slopes: | $[\frac{4}{3},\frac{4}{3},2,2]$ |
| Swan slopes: | $[3]$ |
| Means: | $\langle\frac{3}{2}\rangle$ |
| Rams: | $(3)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $12$ |
| Absolute Mass: | $3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.