Growth of torsion of elliptic curves with full 2-torsion over quadratic cyclotomic fields

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• 作者：Burton Newman¹ ; ^{bnewman@usc.edu}
• 关键词：primary ; 11G05 ; secondary ; 14G05
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：173
• 期：Complete
• 页码：570-601
• 全文大小：509 K
• 卷排序：173

文摘

Let K=Q(−3) or Q(−1) and let CnCn denote the cyclic group of order n. We study how the torsion part of an elliptic curve over K grows in a quadratic extension of K  . In the case E(K)[2]≈C2⊕C2E(K)[2]≈C2⊕C2 we determine how a given torsion structure can grow in a quadratic extension and the maximum number of quadratic extensions in which it grows. We also classify the torsion structures which occur as the quadratic twist of a given torsion structure.