On Elliptic Curves Via Heron Triangles and Diophantine Triples

In this article, we construct families of elliptic curves arising from the Heron triangles and Diophantine triples with the Mordell-Weil torsion subgroup of Z/2Z × Z/2Z. These families have ranks at least 2 and 3, respectively, and contain particular examples with rank equal to 7.