Defining polynomial over unramified subextension
| $x^{4} + 8 b_{11} x^{3} + 4 b_{6} x^{2} + 8 b_{9} x + 8 c_{8} + 16 c_{12} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $40$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $10$ |
| Discriminant exponent $c$: | $110$ |
| Artin slopes: | $[3,4]$ |
| Swan slopes: | $[2,3]$ |
| Means: | $\langle1,2\rangle$ |
| Rams: | $(2,4)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $40$ |
| Mass: | $1073741824$ |
| Absolute Mass: | $536870912/5$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.