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arXiv · 1012.5835

A new family of elliptic curves with positive ranks arising from the Heron triangles

F. A. Izadi·Foad Khoshnam·K. Nabardi
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Abstract

The aim of this paper is to introduce a new family of elliptic curves with positive ranks. These elliptic curves have been constructed with certain rational numbers, namely a, b, and c as sides of Heron triangles having rational areas $k$. It turned out that the torsion groups of this family are of the form $\frac{\Bbb{Z}}{2\Bbb{Z}}\times \frac{\Bbb{Z}}{2\Bbb{Z}}$ and also the rank is positive.

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F. A. Izadi, Foad Khoshnam, K. Nabardi. 2010-12-28. A new family of elliptic curves with positive ranks arising from the Heron triangles. https://arxiv.org/abs/1012.5835

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