论文标题
由理性双苯胺诱导的零椭圆曲线零椭圆形曲线
Rank zero elliptic curves induced by rational Diophantine triples
论文作者
论文摘要
理性的双三元三联物，即AB+1，AC+1，BC+1的属性的理性A，B，C是完美的正方形，通常用于构造高等级的椭圆形曲线。在本文中，我们考虑了相反的问题，并询问有理由双三联剂引起的椭圆曲线的等级有多小。很容易找到具有混合符号的元素的理性双三元组，这些元素诱导椭圆形曲线具有等级0。但是，找到具有正面元素的理性二氧化三联剂示例的问题更具挑战性，我们将提供第一个此类已知示例。
Rational Diophantine triples, i.e. rationals a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares, are often used in construction of elliptic curves with high rank. In this paper, we consider the opposite problem and ask how small can be the rank of elliptic curves induced by rational Diophantine triples. It is easy to find rational Diophantine triples with elements with mixed signs which induce elliptic curves with rank 0. However, the problem of finding such examples of rational Diophantine triples with positive elements is much more challenging, and we will provide the first such known example.
