Defining polynomial over unramified subextension
| $x^{8} + 4 a_{15} x^{7} + 4 b_{14} x^{6} + \left(2 a_{4} + 8 c_{20}\right) x^{4} + 8 b_{19} x^{3} + 4 a_{10} x^{2} + 8 b_{17} x + 4 c_{8} + 8 c_{16} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $32$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $4$ |
| Discriminant exponent $c$: | $88$ |
| Artin slopes: | $[2,3,\frac{7}{2}]$ |
| Swan slopes: | $[1,2,\frac{5}{2}]$ |
| Means: | $\langle\frac{1}{2},\frac{5}{4},\frac{15}{8}\rangle$ |
| Rams: | $(1,3,5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $13824000$ |
| Absolute Mass: | $3456000$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.