There are infinitely many elliptic curves over the rationals of rank 2

2025/02/04 by Zywina, David · 3 citations
#11G18 (Primary) 14J27 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.01957

Abstract

We show that there are infinitely many elliptic curves E/ℚ, up to isomorphism over ℚ, for which the finitely generated group E(ℚ) has rank exactly 2. Our elliptic curves are given by explicit models and their rank is shown to be 2 via a 2-descent. That there are infinitely many such elliptic curves makes use of a theorem of Tao and Ziegler.

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