A Note On Elliptic Plane Curves With Fixed j-Invariant

1995/05/24 by Rahul Pandharipande, R. Pandharipande, Pandharipande, R. · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9505023

10 pages, AMSLatex

arxiv created 1995/05/24 · openalex publication_date 1995/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let N_d be the number of degree d, nodal, rational plane curves through 3d-1 points in the complex projective plane. The number of degree d>=3, nodal, elliptic plane curves with a fixed (general) j-invariant through 3d-1 points is found to be d-1 \choose 2*N_d.

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