Computation on elliptic curves with complex multiplication

被引：27

作者：

Clark, Pete L. ^{[1
]}

Corn, Patrick ^{[2
]}

Rice, Alex ^{[3
]}

Stankewicz, James ^{[4
]}

机构：

[1] Univ Georgia, Athens, GA 30602 USA

[2] Virtu Financial, Austin, TX 78746 USA

[3] Bucknell Univ, Lewisburg, PA 17837 USA

[4] Univ Copenhagen, DK-2100 Copenhagen, Denmark

来源：

LMS JOURNAL OF COMPUTATION AND MATHEMATICS | 2014年 / 17卷 / 01期

关键词：

INTEGRAL J-INVARIANT; TORSION POINTS; BOUNDS;

D O I：

10.1112/S1461157014000072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1-13. Additionally we describe the algorithm used to compute these torsion subgroups and its implementation.

引用

页码：509 / 535

页数：27

共 25 条

[11] TORSION POINTS ON ELLIPTIC-CURVES AND Q-COEFFICIENTS OF MODULAR-FORMS [J].

KAMIENNY, S .

INVENTIONES MATHEMATICAE, 1992, 109 (02) :221-229

[12] TORSION POINTS ON ELLIPTIC-CURVES DEFINED OVER QUADRATIC FIELDS [J].

KENKU, MA ;

MOMOSE, F .

NAGOYA MATHEMATICAL JOURNAL, 1988, 109 :125-149

[13]

KUBERT DS, 1976, P LOND MATH SOC, V33, P193

[14]

Mazur B., 1977, PUBL MATH-PARIS, V47, P33, DOI [DOI 10.1007/BF02684339, 10.1007/BF02684339]

[15] Bounds for torsion points on elliptic curves over number fields [J].

Merel, L .

INVENTIONES MATHEMATICAE, 1996, 124 (1-3) :437-449

[16]

Milne J., CLASS FIELD THEORY V

[17]

MULLER HH, 1989, J REINE ANGEW MATH, V397, P100

[18] POINTS OF FINITE ORDER ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION [J].

OLSON, LD .

MANUSCRIPTA MATHEMATICA, 1974, 14 (02) :195-205

[19] Torsion groups of elliptic curves with integral j-invariant over general cubic number fields [J].

Petho, A ;

Weis, T ;

Zimmer, HG .

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 1997, 7 (03) :353-413

[20]

Prasad Dipendra., 2001, C. R. Math. Acad. Sci. Soc. R. Can, V23, P1

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