Group structure of elliptic curves over finite fields

被引：16

作者：

Wittmann, C ^{[1
]}

机构：

[1] Univ Bundeswehr Munchen, Fak Informat, Inst Theoret Informat & Math, D-85577 Neubiberg, Germany

来源：

JOURNAL OF NUMBER THEORY | 2001年 / 88卷 / 02期

关键词：

elliptic curves; finite fields;

D O I：

10.1006/jnth.2000.2622

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a finite abelian group such that there is an elliptic curve defined over a finite field F-q with E(F-q) congruent to A. We will determine the possible group structures E(F-q(k)) as E varies over all elliptic curves defined over F-q with E(F-q) congruent to A. (C) 2001 Academic Press.

引用

页码：335 / 344

页数：10

共 50 条

[21] The critical groups of a family of graphs and elliptic curves over finite fields [J].

Gregg Musiker .

Journal of Algebraic Combinatorics, 2009, 30 :255-276

[22] The critical groups of a family of graphs and elliptic curves over finite fields [J].

Musiker, Gregg .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2009, 30 (02) :255-276

[23] The group structures of automorphism groups of elliptic curves over finite fields and their applications to optimal locally repairable codes [J].

Ma, Liming ;

Xing, Chaoping .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2023, 193

[24] LOCAL-GLOBAL ASPECTS OF (HYPER)ELLIPTIC CURVES OVER (IN)FINITE FIELDS [J].

Silverman, Joseph H. .

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2010, 4 (02) :101-114

[25] Elliptic Curves over a Finite Ring [J].

Cheddour, Zakariae ;

Chillali, Abdelhakim ;

Mouhib, Ali .

ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2023, 50 (02) :313-324

[26] ELEMENTS OF HIGH ORDER ON FINITE FIELDS FROM ELLIPTIC CURVES [J].

Voloch, Jose Felipe .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2010, 81 (03) :425-429

[27] High rank elliptic curves with prescribed torsion group over quadratic fields [J].

Aguirre, Julian ;

Dujella, Andrej ;

Bokun, Mirela Jukic ;

Carlos Peral, Juan .

PERIODICA MATHEMATICA HUNGARICA, 2014, 68 (02) :222-230

[28] High rank elliptic curves with prescribed torsion group over quadratic fields [J].

Julián Aguirre ;

Andrej Dujella ;

Mirela Jukić Bokun ;

Juan Carlos Peral .

Periodica Mathematica Hungarica, 2014, 68 :222-230

[29] Torsion of elliptic curves over cubic fields [J].

Najman, Filip .

JOURNAL OF NUMBER THEORY, 2012, 132 (01) :26-36

[30] EXCEPTIONAL ELLIPTIC CURVES OVER QUARTIC FIELDS [J].

Najman, Filip .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (05) :1231-1246

← 1 2 3 4 5 →