ELLIPTIC CURVES WITH COMMON TORSION x-COORDINATES AND HYPERELLIPTIC TORSION PACKETS

被引：1

作者：

Fu, Hang ^{[1
]}

Stoll, Michael ^{[2
]}

机构：

[1] Natl Taiwan Univ, Dept Math, Taipei, Taiwan

[2] Univ Bayreuth, Math Inst, D-95440 Bayreuth, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 12期

关键词：

Elliptic curves; torsion points; hyperelliptic curves; torsion packets;

D O I：

10.1090/proc/16102

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a connection between torsion packets on curves of genus 2 and pairs of elliptic curves realized as double covers of the projective line P-x(1) that have many common torsion x-coordinates. This can be used to show that the set of common torsion x-coordinates has size at least 22 infinitely often and has 34 elements in some cases. We also explain how we obtained the current record example of a hyperelliptic torsion packet on a genus 2 curve.

引用

页码：5137 / 5149

页数：13

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