Defining polynomial over unramified subextension
| $x^{12} + 4 b_{23} x^{11} + 2 a_{10} x^{10} + 4 b_{21} x^{9} + 4 c_{20} x^{8} + 4 b_{19} x^{7} + 4 b_{18} x^{6} + 4 a_{17} x^{5} + 4 b_{14} x^{2} + 2 d_{0} + 8 c_{24}$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $24$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $12$ |
| Residue field degree $f$: | $2$ |
| Discriminant exponent $c$: | $56$ |
| Artin slopes: | $[\frac{8}{3},3]$ |
| Swan slopes: | $[\frac{5}{3},2]$ |
| Means: | $\langle\frac{5}{6},\frac{17}{12}\rangle$ |
| Rams: | $(5,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $24$ |
| Mass: | $9216$ |
| Absolute Mass: | $4608$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.