Defining polynomial
| $x^{4} + \left(b_{15} \pi^{4} + b_{11} \pi^{3}\right) x^{3} + a_{2} \pi x^{2} + \left(b_{13} \pi^{4} + a_{9} \pi^{3}\right) x + c_{16} \pi^{5} + c_{4} \pi^{2} + \pi$ |
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 $c$: | $12$ |
| Absolute Artin slopes: | $[2,3,4,4,\frac{17}{4}]$ |
| Swan slopes: | $[1,4]$ |
| Means: | $\langle\frac{1}{2},\frac{9}{4}\rangle$ |
| Rams: | $(1,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $8$ |
| Absolute Mass: | $4$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.