Elliptic surfaces and contact conics for a 3-nodal quartic

Let Q be an irreducible 3-nodal quartic and let C be a smooth conic such that C boolean AND Q does not contain any node of Q and the intersection multiplicity at z is an element of C boolean AND Q is even for each z. In this paper, we study geometry of C vertical bar Q through that of integral sections of a rational elliptic surface which canonically arises from Q and z is an element of C boolean AND Q. As an application, we construct Zariski pairs (C-1 + Q, C-2 + Q), where C-i (i = 1, 2) are smooth conics tangent to Q at four distinct points.