Defining polynomial
| $x^{28} + 4 c_{52} x^{24} + 4 b_{51} x^{23} + 4 b_{49} x^{21} + 4 b_{47} x^{19} + 4 b_{45} x^{17} + 4 b_{43} x^{15} + 4 b_{41} x^{13} + 2 c_{12} x^{12} + 4 b_{39} x^{11} + 2 b_{10} x^{10} + 4 b_{37} x^{9} + 4 b_{35} x^{7} + 2 a_{6} x^{6} + 4 b_{33} x^{5} + 4 b_{31} x^{3} + 4 a_{29} x + 2$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $28$ |
| Base field: | $\Q_{2}$ |
| Ramification index $e$: | $28$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $56$ |
| Artin slopes: | $[\frac{10}{7},\frac{20}{7}]$ |
| Swan slopes: | $[\frac{3}{7},\frac{13}{7}]$ |
| Means: | $\langle\frac{3}{14},\frac{29}{28}\rangle$ |
| Rams: | $(3,23)$ |
| 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.