Defining polynomial
| $x^{4} + \left(b_{43} \pi^{11} + b_{39} \pi^{10} + b_{35} \pi^{9} + a_{31} \pi^{8}\right) x^{3} + \left(b_{34} \pi^{9} + b_{30} \pi^{8} + b_{26} \pi^{7} + b_{22} \pi^{6} + a_{18} \pi^{5}\right) x^{2} + \left(b_{41} \pi^{11} + b_{37} \pi^{10} + b_{33} \pi^{9}\right) x + c_{44} \pi^{12} + c_{36} \pi^{10} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.20d1.10 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $34$ |
| Absolute Artin slopes: | $[2,3,3,\frac{15}{4},4]$ |
| Swan slopes: | $[9,11]$ |
| Means: | $\langle\frac{9}{2},\frac{31}{4}\rangle$ |
| Rams: | $(9,13)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $1024$ |
| Absolute Mass: | $256$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.