Defining polynomial
| $x^{28} + 2 b_{26} x^{26} + 4 c_{52} x^{24} + 4 b_{51} x^{23} + 2 b_{22} x^{22} + 4 b_{49} x^{21} + 4 b_{47} x^{19} + 2 a_{18} x^{18} + 4 b_{45} x^{17} + 4 b_{43} x^{15} + 4 b_{41} x^{13} + 4 b_{39} x^{11} + 4 b_{37} x^{9} + 4 c_{36} x^{8} + 4 a_{35} x^{7} + 4 b_{34} x^{6} + 4 b_{30} x^{2} + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $28$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $28$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $62$ |
| Artin slopes: | $[\frac{16}{7},\frac{20}{7}]$ |
| Swan slopes: | $[\frac{9}{7},\frac{13}{7}]$ |
| Means: | $\langle\frac{9}{14},\frac{5}{4}\rangle$ |
| Rams: | $(9,17)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $4096$ |
| Absolute Mass: | $4096$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.