On the torsion group of elliptic curves induced by D(4)-triples

A D(4)-m-tuple is a set of m integers such that the product of any two of them increased by 4 is a perfect square. A problem of extendibility of D(4)-m-tuples is closely connected with the properties of elliptic curves associated with them. In this paper we prove that the torsion group of an elliptic curve associated with a D(4)-triple can be either Z/2Z × Z/2Z or Z/2Z × Z/6Z, except for the D(4)-triple {; ; ; ; −1, 3, 4}; ; ; ; when the torsion group is Z/2Z × Z/4Z.