Defining polynomial over unramified subextension
| $x^{8} + 2 b_{7} x^{7} + 2 a_{5} x^{5} + 2 a_{2} x^{2} + 4 c_{8} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $48$ |
| Artin slopes: | $[\frac{4}{3},\frac{4}{3},2]$ |
| Swan slopes: | $[\frac{1}{3},\frac{1}{3},1]$ |
| Means: | $\langle\frac{1}{6},\frac{1}{4},\frac{5}{8}\rangle$ |
| Rams: | $(\frac{1}{3},\frac{1}{3},3)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $3600$ |
| Absolute Mass: | $900$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.