由理性丢番图三元组诱导的高阶椭圆曲线

IF 0.5 4区数学 Q3 MATHEMATICS

Glasnik Matematicki Pub Date : 2020-05-21 DOI:10.3336/gm.55.2.05

A. Dujella, J. C. Peral

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引用次数: 3

摘要

有理数Diophantine三元组是由三个非零有理数A,b,c组成的集合，具有ab+1, ac+1, bc+1是完全平方的性质。我们说椭圆曲线y2 = (ax+1)(bx+1)(cx+1)是由三元{a,b,c}导出的。在有理丢番图三元组参数化的基础上，给出了构造合理高阶椭圆曲线的一种新方法。特别地，我们构造了一条秩为12的有理Diophantine三重体诱导的椭圆曲线，以及秩≥7的椭圆曲线的无限族，这两条曲线都是这类曲线的现有记录。

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High rank elliptic curves induced by rational Diophantine triples

A rational Diophantine triple is a set of three nonzero rational a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares. We say that the elliptic curve y2 = (ax+1)(bx+1)(cx+1) is induced by the triple {a,b,c}. In this paper, we describe a new method for construction of elliptic curves over ℚ with reasonably high rank based on a parametrization of rational Diophantine triples. In particular, we construct an elliptic curve induced by a rational Diophantine triple with rank equal to 12, and an infinite family of such curves with rank ≥ 7, which are both the current records for that kind of curves.

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来源期刊

Glasnik Matematicki MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Glasnik Matematicki publishes original research papers from all fields of pure and applied mathematics. The journal is published semiannually, in June and in December.