High rank elliptic curves induced by rational Diophantine triples

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