Non-trivial Shafarevich-Tate Groups of Elliptic Curves

2017/03/17 by Zhangjie Wang, Wang, Zhangjie
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.05909

openalex publication_date 2017/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize quadratic twists of y²=x(x-a²)(x+b²) with Mordell-Weil groups and 2-primary part of Shafarevich-Tate groups being isomorphic to (\mathb Z/2\mathbb Z)² under certain conditions. We also obtain the distribution result of these elliptic curves.

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