Defining polynomial over unramified subextension
| $x^{8} + 8 b_{23} x^{7} + 4 b_{14} x^{6} + 8 b_{21} x^{5} + \left(2 a_{4} + 8 c_{20}\right) x^{4} + 8 a_{19} x^{3} + \left(8 b_{18} + 16 c_{26}\right) x^{2} + 16 b_{25} x + 4 c_{8} + 2$ |
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: | $[2,\frac{7}{2},\frac{17}{4}]$ |
| Swan slopes: | $[1,\frac{5}{2},\frac{13}{4}]$ |
| Means: | $\langle\frac{1}{2},\frac{3}{2},\frac{19}{8}\rangle$ |
| Rams: | $(1,4,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $32$ |
| Mass: | $235929600$ |
| Absolute Mass: | $58982400$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.