Defining polynomial
| $x^{4} + \left(b_{39} \pi^{10} + b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7} + b_{23} \pi^{6}\right) x^{3} + a_{2} \pi x^{2} + \left(b_{37} \pi^{10} + b_{33} \pi^{9} + b_{29} \pi^{8} + b_{25} \pi^{7} + a_{21} \pi^{6}\right) x + c_{40} \pi^{11} + c_{4} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.20a1.2 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $24$ |
| Absolute Artin slopes: | $[2,\frac{20}{7},\frac{20}{7},\frac{20}{7},\frac{31}{8}]$ |
| Swan slopes: | $[1,10]$ |
| Means: | $\langle\frac{1}{2},\frac{21}{4}\rangle$ |
| Rams: | $(1,19)$ |
| 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.