Defining polynomial
| $x^{4} + \left(b_{19} \pi^{5} + b_{15} \pi^{4}\right) x^{3} + \left(b_{10} \pi^{3} + a_{6} \pi^{2}\right) x^{2} + \left(b_{17} \pi^{5} + a_{13} \pi^{4}\right) x + c_{20} \pi^{6} + c_{12} \pi^{4} + \pi$ |
Invariants
| Residue field characteristic: | $2$ |
| Degree: | $4$ |
| Base field: | 2.1.8.20a1.2 |
| Ramification index $e$: | $4$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $16$ |
| Absolute Artin slopes: | $[\frac{20}{7},\frac{20}{7},\frac{20}{7},3,\frac{13}{4}]$ |
| Swan slopes: | $[3,5]$ |
| Means: | $\langle\frac{3}{2},\frac{13}{4}\rangle$ |
| Rams: | $(3,7)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $4$ |
| Mass: | $16$ |
| Absolute Mass: | $16$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.