Elliptic curves of high rank with nontrivial torsion group over Q

被引：5

作者：

Kulesz, L

Stahlke, C

机构：

[1] Univ Paris 07, UFR Math, F-75251 Paris, France

[2] Univ Bonn, Math Inst, D-53115 Bonn, Germany

来源：

EXPERIMENTAL MATHEMATICS | 2001年 / 10卷 / 03期

关键词：

D O I：

10.1080/10586458.2001.10504464

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct elliptic curves over Q of high Mordell-Weil rank, with a nontrivial torsion subgroup. We improve the rank records for the cases Z/2Z x Z/2Z, Z/3Z, Z/4Z, Z/5Z, Z/6Z, Z/7Z and Z/8Z.

引用

页码：475 / 480

页数：6

共 50 条

[1] Families of elliptic curves of high rank with nontrivial torsion group over Q
Kulesz, L
ACTA ARITHMETICA, 2003, 108 (04) : 339 - 356
[2] Construction of high-rank elliptic curves with a nontrivial torsion point
Nagao, K
MATHEMATICS OF COMPUTATION, 1997, 66 (217) : 411 - 415
[3] Diophantine triples and construction of high-rank elliptic curves over Q with three nontrivial 2-torsion points
Dujella, A
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2000, 30 (01) : 157 - 164
[4] High rank elliptic curves with prescribed torsion group over quadratic fields
Aguirre, Julian
Dujella, Andrej
Bokun, Mirela Jukic
Carlos Peral, Juan
PERIODICA MATHEMATICA HUNGARICA, 2014, 68 (02) : 222 - 230
[5] High rank elliptic curves with prescribed torsion group over quadratic fields
Julián Aguirre
Andrej Dujella
Mirela Jukić Bokun
Juan Carlos Peral
Periodica Mathematica Hungarica, 2014, 68 : 222 - 230
[6] Construction of high rank elliptic curves over Q(t) and Q with non-trivial 2-torsion.
Fermigier, S
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1996, 322 (10): : 949 - 952
[7] High rank elliptic curves with torsion group Z/(2Z)
Aguirre, J
Castañeda, F
Peral, JC
MATHEMATICS OF COMPUTATION, 2004, 73 (245) : 323 - 331
[8] Construction of high-rank elliptic curves over Q and Q(t) with non-trivial 2-torsion
Fermigier, S
ALGORITHMIC NUMBER THEORY, 1996, 1122 : 115 - 120
[9] Construction of high-rank elliptic curves over Q and Q(t) with non-trivial 2-torsion
Fermigier, S.
Lecture Notes in Computer Science, 1122
[10] Torsion groups of elliptic curves over Q(μp∞)
Guzvic, Tomislav
Vukorepa, Borna
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2023, 19 (08) : 1745 - 1761

← 1 2 3 4 5 →