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A rational Diophantine triple is a set of three nonzero rational a,b,c withthe property that ab+1, ac+1, bc+1 are perfect squares. We say that theelliptic curve y^2 = (ax+1)(bx+1)(cx+1) is induced by the triple {a,b,c}. Inthis paper, we describe a new method for construction of elliptic curves over Qwith reasonably high rank based on a parametrization of rational Diophantinetriples. In particular, we construct an elliptic curve induced by a rationalDiophantine triple with rank equal to 12, and an infinite family of such curveswith rank >= 7, which are both the current records for that kind of curves.

High rank elliptic curves induced by rational Diophantine triples