On elliptic curves via Heron triangles and Diophantine triples

foad khoshnam


In this article, we construct families of elliptic curves arising from the Heron triangles and Diophantine triples with the Mordell-Weil torsion subgroup of $\Bbb{Z}/2\Bbb{Z}\times\Bbb{Z}/2\Bbb{Z}$.

These families  have ranks at least 2 and 3, respectively, and contain particular examples with rank equal to $7$.


Diophantine triple, elliptic curve, family of elliptic curves, the Heron triangle, specialization, rank, torsion group

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