Sections on certain j=0 elliptic surfaces

1999/11/30 by Jasbir Chahal, J. S. Chahal, Matthijs Meijer +4
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/9911274

arxiv created 1999/11/30 · openalex publication_date 1999/11/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using some theory of (rational) elliptic surfaces plus elementary properties of a Mordell-Weil group regarded as module over the endomorphism ring of a (CM) elliptic curve, we present examples of such surfaces with j-invariant zero. In particular, a K3 example is given with the maximal possible rank 18, plus that many explicit independent sections on it. Several other high rank cases are discussed; for instance Shioda's example with rank 68.

Related

• Rational curves on elliptic surfaces
• Elliptic Surfaces
• Hashing to elliptic curves of j=0 and Mordell--Weil groups
• Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group
• Determining explicitly the Mordell-Weil group of certain rational elliptic surfaces