Defining polynomial
| $x^{24} + 4 b_{47} x^{23} + 4 b_{45} x^{21} + 2 b_{20} x^{20} + 4 b_{43} x^{19} + 4 b_{41} x^{17} + 4 c_{40} x^{16} + 4 a_{39} x^{15} + 4 b_{38} x^{14} + 4 b_{36} x^{12} + 4 b_{34} x^{10} + 4 a_{30} x^{6} + 4 b_{28} x^{4} + 8 c_{48} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $24$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $24$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $62$ |
| Artin slopes: | $[\frac{8}{3},\frac{8}{3},3]$ |
| Swan slopes: | $[\frac{5}{3},\frac{5}{3},2]$ |
| Means: | $\langle\frac{5}{6},\frac{5}{4},\frac{13}{8}\rangle$ |
| Rams: | $(5,5,9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $512$ |
| Absolute Mass: | $512$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.