Torsion points on elliptic curves over number fields of small degree

被引：8

作者：

Derickx, Maarten ^{[1
]}

Kamienny, Sheldon ^{[2
]}

Stein, William ^{[3
]}

Stoll, Michael ^{[4
]}

机构：

[1] Leiden Univ, Math Inst, Leiden, Netherlands

[2] USC Dornsife, Dept Math, Los Angeles, CA USA

[3] SageMath Inc, Renton, WA USA

[4] Univ Bayreuth, Math Inst, Bayreuth, Germany

来源：

ALGEBRA & NUMBER THEORY | 2023年 / 17卷 / 02期

关键词：

elliptic curve; torsion point; torsion subgroup; number fields of small degree; FAMILIES; BOUNDS;

D O I：

10.2140/ant.2023.17.267

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the set S(d) of possible prime orders of K-rational points on elliptic curves over number fields K of degree d for d = 4, 5, 6, and 7.

引用

页码：267 / 308

页数：43

共 50 条

[41] FAMILIES OF ELLIPTIC CURVES OVER CUBIC NUMBER FIELDS WITH PRESCRIBED TORSION SUBGROUPS
Jeon, Daeyeol
Kim, Chang Heon
Lee, Yoonjin
MATHEMATICS OF COMPUTATION, 2011, 80 (273) : 579 - 591
[42] A criterion to rule out torsion groups for elliptic curves over number fields
Bruin P.
Najman F.
Research in Number Theory, 2 (1)
[43] On torsion subgroups of elliptic curves over quartic, quintic and sextic number fields
Kazancioglu, Mustafa Umut
Sadek, Mohammad
JOURNAL OF NUMBER THEORY, 2025, 274 : 37 - 55
[44] TORSION OF ELLIPTIC CURVES OVER IMAGINARY QUADRATIC FIELDS OF CLASS NUMBER 1
Sarma, Naba Kanta
Saikia, Anupam
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2018, 48 (08) : 2689 - 2703
[45] The rank of elliptic curves with rational 2-torsion points over large fields
Im, BH
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (06) : 1623 - 1630
[46] TORSION POINTS ON ELLIPTIC-CURVES OVER ALL QUADRATIC FIELDS .2.
KAMIENNY, S
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1986, 114 (01): : 114 - 122
[47] P-TORSION POINTS ON ELLIPTIC-CURVES DEFINED OVER QUADRATIC FIELDS
MOMOSE, F
NAGOYA MATHEMATICAL JOURNAL, 1984, 96 (DEC) : 139 - 165
[48] On the class numbers of the fields of the pn-torsion points of elliptic curves over Q
Sairaiji, Fumio
Yamauchi, Takuya
JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2018, 30 (03): : 893 - 915
[49] TORSION POINTS OF ELLIPTIC CURVES OVER LARGE ALGEBRAIC EXTENSIONS OF FINITELY GENERATED FIELDS
GEYER, WD
JARDEN, M
ISRAEL JOURNAL OF MATHEMATICS, 1978, 31 (3-4) : 257 - 297
[50] TORSION POINTS ON ELLIPTIC CURVES OVER A GLOBAL FIELD
ZIMMER, HG
MANUSCRIPTA MATHEMATICA, 1979, 29 (2-4) : 119 - 145

← 1 2 3 4 5 →