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

[31] On the cyclic torsion of elliptic curves over cubic number fields (II)
Wang, Jian
JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2019, 31 (03): : 663 - 670
[32] TORSION SUBGROUPS OF ELLIPTIC CURVES OVER QUINTIC AND SEXTIC NUMBER FIELDS
Derickx, Maarten
Sutherland, Andrew V.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (10) : 4233 - 4245
[33] Torsion of rational elliptic curves over quartic Galois number fields
Chou, Michael
JOURNAL OF NUMBER THEORY, 2016, 160 : 603 - 628
[34] A Remark on Elliptic Curves with a Given Number of Points over Finite Fields
Parks, James
SCHOLAR - A SCIENTIFIC CELEBRATION HIGHLIGHTING OPEN LINES OF ARITHMETIC RESEARCH, 2015, 655 : 165 - 179
[35] DIVISION POINTS OF ELLIPTIC CURVES AND ABELLIAN FUNCTIONS OVER NUMBER FIELDS
LANG, S
AMERICAN JOURNAL OF MATHEMATICS, 1975, 97 (01) : 124 - 132
[36] Darmon points on elliptic curves over number fields of arbitrary signature
Guitart, Xavier
Masdeu, Marc
Senguen, Mehmet Haluk
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 111 : 484 - 518
[37] Torsion of elliptic curves over cubic fields
Najman, Filip
JOURNAL OF NUMBER THEORY, 2012, 132 (01) : 26 - 36
[38] Torsion of elliptic curves over cubic fields
Parent, P
ANNALES DE L INSTITUT FOURIER, 2000, 50 (03) : 723 - +
[39] FAMILIES OF ELLIPTIC CURVES OVER CYCLIC CUBIC NUMBER FIELDS WITH PRESCRIBED TORSION
Jeon, Daeyeol
MATHEMATICS OF COMPUTATION, 2016, 85 (299) : 1485 - 1502
[40] FAMILIES OF ELLIPTIC CURVES OVER QUARTIC NUMBER FIELDS WITH PRESCRIBED TORSION SUBGROUPS
Jeon, Daeyeol
Kim, Chang Heon
Lee, Yoonjn
MATHEMATICS OF COMPUTATION, 2011, 80 (276) : 2395 - 2410

← 1 2 3 4 5 →