“…We say that this elliptic curve is induced by the rational Diophantine triple {a, b, c}. The question of possible Mordell-Weil groups of such elliptic curve over Q, Q(t) and quadratic fields, was considered in several papers (see [1,5,8,13,19,20,21,22,23,32]). In particular, it is shown in [8] that all four torsion groups that are allowed by Mazur's theorem for elliptic curves with full 2-torsion, i.e.…”