Defining polynomial
| $x^{4} + \left(b_{51} \pi^{13} + b_{47} \pi^{12} + b_{43} \pi^{11} + b_{39} \pi^{10} + b_{35} \pi^{9} + b_{31} \pi^{8}\right) x^{3} + \left(b_{10} \pi^{3} + a_{6} \pi^{2}\right) x^{2} + \left(b_{49} \pi^{13} + b_{45} \pi^{12} + b_{41} \pi^{11} + b_{37} \pi^{10} + b_{33} \pi^{9} + a_{29} \pi^{8}\right) x + c_{52} \pi^{14} + c_{12} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.7.6a1.1 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $32$ |
| Absolute Artin slopes: | $[\frac{10}{7},\frac{20}{7}]$ |
| Swan slopes: | $[3,13]$ |
| Means: | $\langle\frac{3}{2},\frac{29}{4}\rangle$ |
| 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.