Torsion groups of elliptic curves over quadratic fields

被引：24

作者：

Kamienny, Sheldon ^{[1
]}

Najman, Filip ^{[2
,3
]}

机构：

[1] Univ So Calif, Dept Math, 3620 S Vermont Ave, Los Angeles, CA 90089 USA

[2] Math Inst, NL-2300 RA Leiden, Netherlands

[3] Univ Zagreb, Dept Math, Zagreb 10000, Croatia

来源：

ACTA ARITHMETICA | 2012年 / 152卷 / 03期

关键词：

torsion group; elliptic curves; quadratic fields; MODULAR L-FUNCTIONS; NUMBER-FIELDS; POINTS; TWISTS;

D O I：

10.4064/aa152-3-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

[No abstract available]

引用

页码：291 / 305

页数：15

共 18 条

[1] EQUATIONS FOR THE MODULAR CURVE X1(N) AND MODELS OF ELLIPTIC CURVES WITH TORSION POINTS [J].

Baaziz, Houria .

MATHEMATICS OF COMPUTATION, 2010, 79 (272) :2371-2386

[2]

Dujella A., INFINITE FAMILIES EL

[3] ON J1(P) AND THE CONJECTURE OF BIRCH AND SWINNERTON DYER [J].

KAMIENNY, S .

DUKE MATHEMATICAL JOURNAL, 1982, 49 (02) :329-340

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

KAMIENNY, S .

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

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

KENKU, MA ;

MOMOSE, F .

NAGOYA MATHEMATICAL JOURNAL, 1988, 109 :125-149

[6] RATIONAL POINTS OF ABELIAN VARIETIES WITH VALUES IN TOWERS OF NUMBER FIELDS [J].

MAZUR, B .

INVENTIONES MATHEMATICAE, 1972, 18 (3-4) :183-266

[7] RATIONAL ISOGENIES OF PRIME DEGREE [J].

MAZUR, B .

INVENTIONES MATHEMATICAE, 1978, 44 (02) :129-162

[8]

Najmam F., 2011, Math J. Okayama U., V53, P75

[9] Complete classification of torsion of elliptic curves over quadratic cyclotomic fields [J].

Najman, Filip .

JOURNAL OF NUMBER THEORY, 2010, 130 (09) :1964-1968

[10] Non-vanishing of quadratic twists of modular L-functions [J].

Ono, K ;

Skinner, C .

INVENTIONES MATHEMATICAE, 1998, 134 (03) :651-660

← 1 2 →