Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves

2008/07/15 by Yuri Bilu, Bilu, Yuri, Pierre Parent +1
Mathematics · #11G05 #11G16 (Secondary) #11G18 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0807.2350

openalex publication_date 2008/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We bound the j -invariant of integral points on a modular curve in terms of the congruence group defining the curve. We apply this to prove that the modular curve Xsplit (p3) has no non-trivial rational point if p is a sufficiently large prime number. Assuming the GRH, one can replace p3 by p2 .

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