  We prove the existence of three irreducible curves $C_{12,m}$ of degree 12
with the same number of cusps and different Alexander polynomials. This
exhibits a Zariski triple. Moreover we provide a set of generators for the
elliptic threefold with constant $j$-invariant 0 and discriminant curve
$C_{12,m}$. Finally we consider general degree $d$ base change of $C_{12d,m}$
and calculate the dimension of the equisingular deformation space.
