Centers for a 6-parameter family of polynomial vector fields of arbitrary degree

For all non-negative integers n1,n2,n3,j1,j2 and j3 with nk+jk>1 for k=1,2,3, (nk,jk)≠(nl,jl) if k≠l, j3=n3−1 and jk≠nk−1 for k=1,2, we study the center variety of the 6-parameter family of real planar polynomial vector given, in complex notation, by , where z=x+iy and A,B,C∈C\{0}.