The order of the torsion group does only depend on the choice of the line in the complete intersection of the quadratic relations Q in the ℙ11 of a-variables. The associated line to a numerical Godeaux surface with a trivial torsion group and no hyperelliptic bicanonical fibers does not intersect any of the special loci in Q. We call such a line a general line in Q. To obtain surfaces with one respectively two hyperelliptic fibers, the corresponding line must intersect the hyperelliptic locus in Q in one respectively two points. The number of hyperelliptic fibers must be between 0 and 2.