Defining polynomial over unramified subextension
| $x^{8} + 8 b_{22} x^{6} + 8 b_{21} x^{5} + 4 b_{12} x^{4} + 8 a_{19} x^{3} + 8 b_{18} x^{2} + 8 c_{16} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $104$ |
| Artin slopes: | $[3,\frac{23}{6},\frac{23}{6}]$ |
| Swan slopes: | $[2,\frac{17}{6},\frac{17}{6}]$ |
| Means: | $\langle1,\frac{23}{12},\frac{19}{8}\rangle$ |
| Rams: | $(2,\frac{11}{3},\frac{11}{3})$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $983040$ |
| Absolute Mass: | $245760$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.