Defining polynomial over unramified subextension
| $x^{8} + 8 b_{23} x^{7} + 8 b_{22} x^{6} + 8 a_{21} x^{5} + 4 b_{12} x^{4} + \left(8 b_{18} + 16 c_{26}\right) x^{2} + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $112$ |
| Artin slopes: | $[3,4,\frac{17}{4}]$ |
| Swan slopes: | $[2,3,\frac{13}{4}]$ |
| Means: | $\langle1,2,\frac{21}{8}\rangle$ |
| Rams: | $(2,4,5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $15728640$ |
| Absolute Mass: | $3932160$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.