Defining polynomial over unramified subextension
| $x^{8} + 2 a_{6} x^{6} + \left(2 b_{4} + 4 c_{12}\right) x^{4} + 4 b_{11} x^{3} + 4 a_{9} x + 4 c_{8} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $24$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $8$ |
| Residue field degree $f$: | $3$ |
| Discriminant exponent $c$: | $48$ |
| Artin slopes: | $[2,2,\frac{5}{2}]$ |
| Swan slopes: | $[1,1,\frac{3}{2}]$ |
| Means: | $\langle\frac{1}{2},\frac{3}{4},\frac{9}{8}\rangle$ |
| Rams: | $(1,1,3)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $24$ |
| Mass: | $3136$ |
| Absolute Mass: | $3136/3$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.