Elliptic K3 surfaces with geometric Mordell-Weil rank 15

2005/02/21 by Remke Kloosterman, Kloosterman, Remke
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0502439

arxiv created 2005/02/21 · openalex publication_date 2005/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the elliptic surface y²=x³+2(t⁸+14t⁴+1)x+4t²(t⁸+6t⁴+1) has geometric Mordell-Weil rank 15. This completes a list of Kuwata, who gave explicit examples of elliptic K3-surfaces with geometric Mordell-Weil rank 0,1,..., 14, 16, 17,18.

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