论文标题
高级椭圆形曲线由理性双苯胺三元组引起
High rank elliptic curves induced by rational Diophantine triples
论文作者
论文摘要
理性的双苯胺三倍是三个非零有理A，b，c，具有AB+1，AC+1，BC+1的特性是完美的正方形。我们说椭圆曲线y^2 =（ax+1）（bx+1）（cx+1）由三重{a，b，c}诱导。在本文中，我们描述了一种基于有理二只三元组的参数化的Q层构建椭圆形曲线的新方法。特别是，我们构建了由等级等于12的有理双苯胺三倍引起的椭圆曲线，而这种曲线的无限家族> = 7，这都是这种曲线的当前记录。
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 y^2 = (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.
