Defining polynomial over unramified subextension
| $x^{8} + 4 b_{14} x^{6} + 4 a_{13} x^{5} + 4 b_{12} x^{4} + 2$ |
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: | $[\frac{20}{7},\frac{20}{7},\frac{20}{7}]$ |
| Swan slopes: | $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]$ |
| Means: | $\langle\frac{13}{14},\frac{39}{28},\frac{13}{8}\rangle$ |
| Rams: | $(\frac{13}{7},\frac{13}{7},\frac{13}{7})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $3840$ |
| Absolute Mass: | $960$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.