Acta Scientiarum Naturalium Universitatis Pekinensis

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Isomorphism Classes of Elliptic Curves with 3-Torsion Point

WU Hongfeng1, FENG Rongquan2, WANG Zilong3   

  1. 1. College of Sciences, North China University of Technology, Beijing 100041; 2. School of Mathematical Sciences, Peking University, Beij ing 100871; 3. Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an 710071;
  • Received:2010-05-15 Online:2010-09-20 Published:2010-09-20



  1. 1.北方工业大学理学院,北京100041; 2.北京大学数学科学学院,北京100871; 3.西安电子科技大学,计算机网络与信息安全教育部重点实验室,西安 710071;

Abstract: The numbers of Fq- isomorphism classes and Fq- isomorphism classes of elliptic curves defined over Fq with a 3- torsion Fq- rational point are enumerated.

Key words: elliptic curves, cryptography, isomorphism classes, j-invariant

摘要: 研究了定义在有限域Fq上含3阶Fq-有理点的椭圆曲线簇的Fq-同构类和Fq-同构类, 并给出了精确的计数公式。

关键词: 椭圆曲线, 密码学, 同构类, j-不变量

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