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Rank computation of elliptic curves has deep relations with various unsolvedquestions in number theory, most notably in the congruent number problem forright-angled triangles. Similar relations between elliptic curves and Herontriangles were established later. In this work, we explicitly compute the2-Selmer rank of the elliptic curves associated with Heron triangles of evenarea, which eventually sheds light on the Mordell-Weil rank of those curves.

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