Defining polynomial
| $x^{4} + \left(b_{19} \pi^{5} + b_{15} \pi^{4} + a_{11} \pi^{3}\right) x^{3} + a_{2} \pi x^{2} + \left(b_{17} \pi^{5} + b_{13} \pi^{4}\right) x + c_{20} \pi^{6} + c_{4} \pi^{2} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.2.4.16b2.8 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $14$ |
| Absolute Artin slopes: | $[2,2,3,\frac{7}{2}]$ |
| Swan slopes: | $[1,5]$ |
| Means: | $\langle\frac{1}{2},\frac{11}{4}\rangle$ |
| Rams: | $(1,9)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $2304$ |
| Absolute Mass: | $576$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.