On elliptic curves via Heron triangles and Diophantine triples

foad khoshnam

Abstract


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 $7$.


Keywords


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

Full Text: PDF

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.