Defining polynomial
| $x^{24} + 4 b_{47} x^{23} + 4 b_{45} x^{21} + 4 b_{43} x^{19} + 4 b_{41} x^{17} + 2 c_{16} x^{16} + 4 b_{39} x^{15} + 2 b_{14} x^{14} + 4 b_{37} x^{13} + 4 b_{35} x^{11} + 2 a_{10} x^{10} + 4 b_{33} x^{9} + 2 c_{8} x^{8} + 4 b_{31} x^{7} + 4 a_{29} x^{5} + 2 a_{4} x^{4} + 8 c_{48} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $24$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $24$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $52$ |
| Artin slopes: | $[\frac{4}{3},\frac{5}{3},3]$ |
| Swan slopes: | $[\frac{1}{3},\frac{2}{3},2]$ |
| Means: | $\langle\frac{1}{6},\frac{5}{12},\frac{29}{24}\rangle$ |
| Rams: | $(1,3,19)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $8$ |
| Mass: | $1024$ |
| Absolute Mass: | $1024$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.