On the cyclic torsion of elliptic curves over cubic number fields

2015/02/24 by Jian Wang, Wang, Jian
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1502.06873

openalex publication_date 2015/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E be an elliptic defined over a number field K. Then its Mordell-Weil group E(K) is finitely generated: E(K)≅ E(K)_tor×ℤ^r. In this paper, we discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. For N=169,143,91,65,77 or 55, we show that ℤ/Nℤ is not a subgroup of E(K)_tor for any elliptic curve E over a cubic number field K.

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