Determining explicitly the Mordell-Weil group of certain rational elliptic surfaces

2025/06/24 by Remke Kloosterman, Kloosterman, Remke · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2506.19423

openalex publication_date 2025/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A,B be nonzero rational numbers. Consider the elliptic curve E_A,B/ℚ(t) with Weierstrass equation y²=x³+At⁶+B. An algorithm to determine rank E_A,B(ℚ(t)) as a function of (A,B) was presented in a recent paper by Desjardins and Naskrecki. We will give a different and shorter proof for the correctness of that algorithm, using a more geometric approach and discuss for which classes of examples this approach might be useful.

Cited by

• Hilbert property for low-genus families and degree-one del Pezzo surfaces

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