Ranks of elliptic curves in families of quadratic twists

1999/12/01 by Karl Rubin, Alice Silverberg, Rubin, Karl +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT

paper · pdf · doi:10.48550/arxiv.math/9912249

arxiv created 1999/12/01 · openalex publication_date 1999/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the unboundedness of the ranks of the quadratic twists of an elliptic curve is equivalent to the divergence of certain infinite series.

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• Constructing Jacobians of rank 1

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