Defining polynomial
| $x^{4} + b_{11} \pi^{3} x^{3} + \left(b_{10} \pi^{3} + b_{6} \pi^{2}\right) x^{2} + a_{9} \pi^{3} x + c_{12} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.10.19a1.39 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $12$ |
| Absolute Artin slopes: | $[\frac{8}{5},\frac{8}{5},3]$ |
| Swan slopes: | $[3,3]$ |
| Means: | $\langle\frac{3}{2},\frac{9}{4}\rangle$ |
| Rams: | $(3,3)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $2$ |
| Mass: | $8$ |
| Absolute Mass: | $4$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.