Elliptic curves associated with Heron triangles with high $2$-Selmer rank

TL;DR

This paper computes the 2-Selmer rank of elliptic curves linked to Heron triangles with even area, providing insights into their Mordell-Weil rank and advancing understanding in number theory.

Contribution

It explicitly calculates the 2-Selmer rank for elliptic curves associated with Heron triangles, a novel step in understanding their Mordell-Weil ranks.

Findings

Explicit 2-Selmer rank computations for specific Heron triangle elliptic curves

Insights into the Mordell-Weil rank related to Heron triangles

Advancement in the number theory connection between Heron triangles and elliptic curves

Abstract

Rank computation of elliptic curves has deep relations with various unsolved questions in number theory, most notably in the congruent number problem for right-angled triangles. Similar relations between elliptic curves and Heron triangles were established later. In this work, we explicitly compute the 2-Selmer rank of the elliptic curves associated with Heron triangles of even area, which eventually sheds light on the Mordell-Weil rank of those curves.