Defining polynomial over unramified subextension
| $x^{8} + 4 b_{15} x^{7} + 4 a_{13} x^{5} + 4 b_{12} x^{4} + 4 a_{10} x^{2} + 8 c_{16} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $80$ |
| Artin slopes: | $[\frac{8}{3},\frac{8}{3},3]$ |
| Swan slopes: | $[\frac{5}{3},\frac{5}{3},2]$ |
| Means: | $\langle\frac{5}{6},\frac{5}{4},\frac{13}{8}\rangle$ |
| Rams: | $(\frac{5}{3},\frac{5}{3},3)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $57600$ |
| Absolute Mass: | $14400$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.