A family of congruent number elliptic curves of rank three

被引：0

作者：

Halbeisen, Lorenz ^{[1
]}

Hungerbuehler, Norbert ^{[1
]}

Zargar, Arman Shamsi ^{[2
]}

机构：

[1] ETH Zentrum, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Univ Mohaghegh Ardabili, Dept Math & Applicat, Ardebil, Iran

来源：

QUAESTIONES MATHEMATICAE | 2023年 / 46卷 / 06期

关键词：

Primary; Secondary; Congruent number; elliptic curve; rank;

D O I：

10.2989/16073606.2022.2058435

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recent progress in the theory of Heron triangles and their elliptic curves led to new families of congruent number elliptic curves with rank at least two. Based on these results, we derive a parametric family of congruent number elliptic curves with rank at least three. It turns out that this family is isomorphic to a family which was recently discovered by the third-named author, however the new approach is simpler, more flexible and gives new insight. In particular, it provides in addition three formulae for congruent numbers.

引用

页码：1131 / 1137

页数：7

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