On elliptic curves induced by rational Diophantine quadruples

被引：1

作者：

Dujella, Andrej ^{[1
]}

Soydan, Gokhan ^{[2
]}

机构：

[1] Univ Zagreb, Fac Sci, Dept Math, Bijenicka Cesta 30, Zagreb 10000, Croatia

[2] Bursa Uludag Univ, Dept Math, TR-16059 Bursa, Turkey

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2022年 / 98卷 / 01期

关键词：

Diophantine quadruples; elliptic curves; torsion group; rank; RANK; CONSTRUCTION; SEXTUPLES; TRIPLES; Q(T);

D O I：

10.3792/pjaa.98.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four non-zero 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 x 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.

引用

页码：1 / 6

页数：6

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