Defining polynomial over unramified subextension
| $x^{8} + 4 a_{15} x^{7} + 4 b_{14} x^{6} + 4 b_{12} x^{4} + 8 b_{17} x + 8 c_{16} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $40$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $5$ |
| Discriminant exponent $c$: | $110$ |
| Artin slopes: | $[3,\frac{19}{6},\frac{19}{6}]$ |
| Swan slopes: | $[2,\frac{13}{6},\frac{13}{6}]$ |
| Means: | $\langle1,\frac{19}{12},\frac{15}{8}\rangle$ |
| Rams: | $(2,\frac{7}{3},\frac{7}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $10$ |
| Mass: | $1015808$ |
| Absolute Mass: | $1015808/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.