The modular curves X0(65) and X0(91) and rational isogeny

1980/01/01 by M. A. Kenku · 3 citations
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · doi:10.1017/s0305004100056462

openalex publication_date 1980/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let N be an integer ≥ 1. The affine modular curve Y 0 ( N ) parameterizes isomorphism classes of pairs ( E; F ), where E is an elliptic curve defined over ℂ, the field of complex numbers, and F is a cyclic subgroup of order N. The compacti-fication X 0 ( N ) is an algebraic curve defined over ℚ.

Cited by

• Isogenies of non-CM elliptic curves with rational j-invariants over\n number fields
• Torsion subgroups of rational elliptic curves over the compositum of all\n D₄ extensions of the rational numbers
• Torsion groups of elliptic curves over some infinite abelian extensions of ℚ

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• On parameterizations of cyclic N-isogenies and strict K-curves lying\n above rational points of Y₀⁺(N)
• Modularity over ℂ implies modularity over ℚ