Defining polynomial
| $x^{4} + \left(b_{27} \pi^{7} + b_{23} \pi^{6} + b_{19} \pi^{5} + a_{15} \pi^{4}\right) x^{3} + a_{2} \pi x^{2} + \left(b_{25} \pi^{7} + b_{21} \pi^{6} + b_{17} \pi^{5}\right) x + c_{28} \pi^{8} + c_{4} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.28b1.22 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $18$ |
| Absolute Artin slopes: | $[2,3,4,\frac{17}{4},\frac{9}{2}]$ |
| Swan slopes: | $[1,7]$ |
| Means: | $\langle\frac{1}{2},\frac{15}{4}\rangle$ |
| Rams: | $(1,13)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $64$ |
| Absolute Mass: | $32$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.