High rank quadratic twists of pairs of elliptic curves

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• 作者：Mohamed Alaa^a ; ^{malaa@sci.cu.edu.eg} ; Mohammad Sadek^b ; ^{mmsadek@aucegypt.edu}
• 关键词：Elliptic curves ; Quadratic twists ; Mordell&ndash ; Weil rank
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：174
• 期：Complete
• 页码：436-444
• 全文大小：273 K
• 卷排序：174

文摘

Given a pair of elliptic curves E1E1 and E2E2 over the rational field QQ whose j-invariants are not simultaneously 0 or 1728, Kuwata and Wang proved the existence of infinitely many square-free rationals d such that the d  -quadratic twists of E1E1 and E2E2 are both of positive rank. We construct infinite families of pairs of elliptic curves E1E1 and E2E2 over QQ such that for each pair there exist infinitely many square-free rationals d for which the d  -quadratic twists of E1E1 and E2E2 are both of rank at least 2.