Heronian elliptic curves and the size of the 2-Selmer group

2023/01/19 by Chakraborty, Debopam, Ghale, Vinodkumar
#11G05 #11G07 (Primary) #51M04 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2301.08099

Abstract

A generalization of the congruent number problem is to find positive integers n that appear as the areas of Heron triangles. Selmer group of a congruent number elliptic curve has been studied quite extensively. Here, we look into the 2-Selmer group structure for Heronian elliptic curves associated with Heron triangles of area n and one of the angle θ such that tan \fracθ2 = n^-1 and n²+1=2q for some prime q.

Related

• Elliptic curves associated with Heron triangles with high 2-Selmer rank
• Heron Quadrilaterals via elliptic curves
• A new family of elliptic curves with positive ranks arising from the Heron triangles
• 2-Selmer Groups and the Birch-Swinnerton-Dyer Conjecture for the Congruent Number Curve
• A Diophantine Criterion for the Shafarevich-Tate Groups of Elliptic Curves from Heron Triangles