An Application of the Arithmetic of Elliptic Curves to the Class Number Problem for Quadratic Fields

被引：4

作者：

Iizuka, Yoshichika ^{[1
]}

Konomi, Yutaka ^{[2
]}

Nakano, Shin ^{[1
]}

机构：

[1] Gakushuin Univ, Dept Math, Toshima Ku, Tokyo 1718588, Japan

[2] Meijo Univ, Dept Math, Tempaku Ku, Nagoya, Aichi 4688502, Japan

来源：

TOKYO JOURNAL OF MATHEMATICS | 2021年 / 44卷 / 01期

关键词：

class number; quadratic field; elliptic curve; POINTS; PAIRS;

D O I：

10.3836/tjm/1502179314

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let l be the prime 3, 5 or 7, and let m(1), m(2), n(1) and n(2) be non-zero rational numbers. We construct an infinite family of pairs of distinct quadratic fields Q(root m(1)D + n(1)) and Q(root m(2)D + n(2)) with D is an element of Q such that both class numbers are divisible by l, using rational points on an elliptic curve with positive Mordell-Weil rank to parametrize such quadratic fields.

引用

页码：33 / 47

页数：15

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