有理丢番图四重体诱导的椭圆曲线

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2021-05-15 DOI:10.3792/pjaa.98.001

A. Dujella, G. Soydan

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引用次数: 2

摘要

在本文中，我们考虑由有理数Diophantine四重组引起的椭圆曲线，即四个非零有理数的集合，其中任意两个的积加1是完全平方。我们证明了对于k = 2,4,6,8的Z/2Z × Z/kZ群，存在无限多个具有诱导椭圆曲线具有此扭转群的有理Diophantine四重组。在这四种情况下，我们还构造了具有中等大秩的曲线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On elliptic curves induced by rational Diophantine quadruples

In this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four nonzero rationals such that the product of any two of them plus 1 is a perfect square. We show that for each of the groups Z/2Z × Z/kZ for k = 2, 4, 6, 8, there are infinitely many rational Diophantine quadruples with the property that the induced elliptic curve has this torsion group. We also construct curves with moderately large rank in each of these four cases.

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来源期刊

Proceedings of the Japan Academy Series A-Mathematical Sciences 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted. The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.