On the cyclic torsion of elliptic curves over cubic number fields

被引：4
作者：
Wang, Jian [1 ,2 ]
机构：
[1] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
JOURNAL OF NUMBER THEORY | 2018年 / 183卷
关键词：
Torsion subgroup; Elliptic curves; Modular curves; POINTS; BOUNDS;
D O I：
10.1016/j.jnt.2017.08.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let E be an elliptic curve defined over a number field K. Then its Mordell-Weil group E(K) is finitely generated: E(K) congruent to E{K)(tor) x 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. (C) 2017 Elsevier Inc. All rights reserved.
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页码：291 / 308
页数：18
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