导子含有三个相异素因子的椭圆曲线  

The Elliptic Curves with the Conductor a Product of Three Distinct Prime Powers

作　　者：蒲可莉 杨仕椿 廖群英 Ke Li PU;Shi Chun YANG;Qun Ying LIAO(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,P.R.China;School of Mathematics,Aba Teachers University,Wenchuan 623000,P.R.China)

机构地区：[1]四川师范大学数学科学学院,成都610066 [2]阿坝师范学院数学学院,汶川623000

出　　处：《数学学报（中文版）》2024年第5期843-858,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(12071321,12361001);四川省科技计划资助项目(2023ZYD0005);阿坝师范学院校级专项项目(AS-RC-ZX2023-03)。

摘　　要：基于Mazur关于扭转子群的完全分类的结论,以及相关丢番图方程正整数解的结果,研究了导子含有三个相异素因子的椭圆曲线,确定了含有阶为n(n≥6,n≠11)的有理点的椭圆曲线,并给出了这些椭圆曲线判别式的上界.Based on the complete classification of the torsion subgroup by Mazur,and results of the related diophantine equation,we determine all elliptic curves defined over Q with a rational point of the order n(n≥6,n≠11)and the conductor p^(a)q^(b)r^(c),where p,q,r are distinct primes,and a,b,c are positive integers.In particular,an upper bound of the minimal discriminant for these elliptic curves are given.

关 键 词：导子 判别式 椭圆曲线 Szpiro猜想 

分 类 号：O186.11[理学—数学]