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.
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页码：5137 / 5149
页数：13
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