Defining polynomial over unramified subextension
| $x^{12} + 2 b_{10} x^{10} + 4 c_{20} x^{8} + 4 b_{19} x^{7} + 2 a_{6} x^{6} + 4 b_{17} x^{5} + 4 b_{15} x^{3} + 4 a_{13} x + 2 d_{0} + 4 c_{12}$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $24$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $12$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $48$ |
| Artin slopes: | $[2,\frac{8}{3}]$ |
| Swan slopes: | $[1,\frac{5}{3}]$ |
| Means: | $\langle\frac{1}{2},\frac{13}{12}\rangle$ |
| Rams: | $(3,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $24$ |
| Mass: | $2304$ |
| Absolute Mass: | $1152$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.