Defining polynomial
| $x^{4} + \left(b_{23} \pi^{6} + b_{19} \pi^{5}\right) x^{3} + \left(b_{14} \pi^{4} + b_{10} \pi^{3}\right) x^{2} + \left(b_{21} \pi^{6} + b_{17} \pi^{5}\right) x + c_{24} \pi^{7} + c_{16} \pi^{5} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.5.2.10a2.1 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $19$ |
| Absolute Artin slopes: | $[2,\frac{7}{2},\frac{9}{2}]$ |
| Swan slopes: | $[4,6]$ |
| Means: | $\langle2,4\rangle$ |
| Rams: | $(4,8)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $1073741824$ |
| Absolute Mass: | $536870912$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.