Defining polynomial
| $x^{4} + \left(b_{47} \pi^{12} + b_{43} \pi^{11} + b_{39} \pi^{10} + b_{35} \pi^{9}\right) x^{3} + \left(b_{30} \pi^{8} + b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5}\right) x^{2} + \left(b_{45} \pi^{12} + b_{41} \pi^{11} + b_{37} \pi^{10} + b_{33} \pi^{9}\right) x + c_{48} \pi^{13} + c_{32} \pi^{9} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.2.4.22a1.16 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $35$ |
| Absolute Artin slopes: | $[3,4,5,6]$ |
| Swan slopes: | $[8,12]$ |
| Means: | $\langle4,8\rangle$ |
| Rams: | $(8,16)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $16777216$ |
| Absolute Mass: | $4194304$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.