Torsion points of elliptic curves over multi-quadratic number fields

被引：0

作者：

Matsuda, Koji ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba,Meguro Ku, Tokyo 1538914, Japan

来源：

JOURNAL OF NUMBER THEORY | 2024年 / 262卷

关键词：

Elliptic curves; Torsion subgroups; Modular curves;

D O I：

10.1016/j.jnt.2024.03.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We compute the Mordell-Weil groups of the modular Jacobian varieties of hyperelliptic modular curves X 1 ( M, MN ) over every composite field of some quadratic number fields. Also we prove criteria for the existence of elliptic curves over such number fields with prescribed torsion points generalizing the results for quadratic number fields of Kamienny and Najman. (c) 2024 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

引用

页码：28 / 43

页数：16

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