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

2023/08/01 by Vinodkumar Ghale, Ghale, Vinodkumar, Md Imdadul Islam +3
Computer Science · Mathematics · #11G07 Secondary: 51M04 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Primary:11G05 #math.NT #msc:11D25 #msc:11G07 #msc:14G25 #msc:14H52 #msc:1G07

paper · pdf · doi:10.48550/arxiv.2308.00625

comments are welcome

openalex publication_date 2023/08/01 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28 · arxiv created 2026/08/03 · arxiv updated 2026/08/04

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.

Related

• Heronian elliptic curves and the size of the 2-Selmer group
• A new family of elliptic curves with positive ranks arising from the Heron triangles
• Heron Quadrilaterals via elliptic curves
• A family of elliptic curves with non-trivial Shafarevich-Tate group
• Finding large Selmer rank via an arithmetic theory of local constants