Defining polynomial over unramified subextension
| $x^{4} + 4 a_{7} x^{3} + \left(4 b_{6} + 8 c_{10}\right) x^{2} + 8 b_{9} x + 8 c_{8} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $8$ |
| Discriminant exponent $c$: | $80$ |
| Artin slopes: | $[3,\frac{7}{2}]$ |
| Swan slopes: | $[2,\frac{5}{2}]$ |
| Means: | $\langle1,\frac{7}{4}\rangle$ |
| Rams: | $(2,3)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $16711680$ |
| Absolute Mass: | $2088960$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.