Rang de courbes elliptiques d'invariant donne

1992/06/16 by Jean-François Mestre, Mestre, Jean-Francois
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.alg-geom/9206007

openalex publication_date 1992/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that there exist infinitely many elliptic curves over \Q with given modular invariant, and rank >=2. Furthermore, there exist infinitely many elliptic curves over \Q with invariant equal at 0 (resp. 1728) and rank >=6 (resp. >=4).

Related

• Infinitely many elliptic curves over ℚ(i) with rank 2 and j-invariant 1728
• There are infinitely many elliptic curves over the rationals of rank 2
• Elliptic curves of rank one over number fields
• Infinite family of elliptic curves of rank at least 4
• Rank one elliptic curves and rank stability