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

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.