Defining polynomial
| $x^{4} + \left(b_{19} \pi^{5} + a_{15} \pi^{4}\right) x^{3} + \left(c_{22} \pi^{6} + b_{14} \pi^{4} + b_{10} \pi^{3}\right) x^{2} + \left(b_{21} \pi^{6} + b_{17} \pi^{5}\right) x + c_{16} \pi^{5} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.4.2.12a1.2 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $18$ |
| Absolute Artin slopes: | $[3,4,\frac{19}{4}]$ |
| Swan slopes: | $[4,\frac{11}{2}]$ |
| Means: | $\langle2,\frac{15}{4}\rangle$ |
| Rams: | $(4,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $15728640$ |
| Absolute Mass: | $1966080$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.