On the Mordell-Weil rank and 2-Selmer group of a family of elliptic curves

2025/03/06 by Pankaj C. Patel, Patel, Pankaj, Debopam Chakraborty +3
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2503.04561

openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the parametric family of elliptic curves over ℚ of the form E_m : y² = x(x - n₁)(x - n₂) + t², where n₁, n₂ and t are particular polynomial expressions in an integral variable m. In this paper, we investigate the torsion group E_m(ℚ)_\rmtors, a lower bound for the Mordell-Weil rank r(E_m) and the 2-Selmer group \rmSel₂(E_m) under certain conditions on m. This extends the previous works done in this direction, which are mostly concerned with the Mordell-Weil ranks of various parametric families of elliptic curves.

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