2025/12/24 by Daeyeol Jeon, Jeon, Daeyeol, Yongjae Kwon +1
Mathematics · #11G05 #11G18 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2512.21088
openalex publication_date 2025/12/24 · openalex created_date 2025/12/26 · openalex updated_date 2026/07/28
The modular curve X0(N) parametrizes elliptic curves together with a cyclic subgroup of order N, and hence cyclic N-isogenies. While explicit moduli descriptions of X1(N) are well developed, a comparable construction for X0(N) has remained incomplete. We give a uniform method for constructing explicit generators of C(X0(N)), extending an approach of Dowd, and use them to obtain a concrete moduli interpretation of cyclic N-isogenies. This yields explicit formulas for sporadic rational points on X0(N) and the associated isogenies, providing a unified solution to the moduli problem for X0(N).