2025/06/26 by Maarten Derickx, Petar Orlić, Derickx, Maarten +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2506.21166
openalex publication_date 2025/06/26 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
Let p be a prime. We study non-constant morphisms f:X0(p)_\mathbb → Y, where Y/\mathbb Q is a curve of genus ≥ 2. We prove that for p<3000 such an f of degree d>1 must be isomorphic to the quotient map X0(p)→ X0+(p). Supported by computational and theoretical evidence, we also conjecture that this is true for all primes p. These results allow us to classify all points of degree ≤ 25 on X0(p) that come from a map to some curve of genus ≥ 2. As an application, we were able to determine all curves X0(p) with infinitely many points of degree 6 over \mathbb Q except for p=193, continuing the previous results on small degree points on X0(N).