On the PGL2-invariant quadruples of torsion points of elliptic curves

被引：0

作者：

Bogomolov, Fedor A. ^{[1
,2
]}

Fu, Hang ^{[3
]}

机构：

[1] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

[2] Natl Res Univ Higher Sch Econ, AG Lab, 6 Usacheva St, Moscow 119048, Russia

[3] Natl Taiwan Univ, Natl Ctr Theoret Sci, Taipei, Taiwan

来源：

EUROPEAN JOURNAL OF MATHEMATICS | 2020年 / 6卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Elliptic curves; Torsion points; q-series; Congruence subgroups; Modular curves; INTERSECTION;

D O I：

10.1007/s40879-019-00377-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E be an elliptic curve and pi : E -> P-1 a standard double cover identifying +/- P. E. It is known that for some torsion points P-i is an element of E, 1 <= i <= 4, the cross ratio of {pi( P-i)}(i=1)(4) is independent of E. We will give a complete classification of such quadruples.

引用

页码：1236 / 1253

页数：18

共 50 条

[1] On the PGL2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{PGL}_{2}$$\end{document}-invariant quadruples of torsion points of elliptic curves
Fedor A. Bogomolov
Hang Fu
European Journal of Mathematics, 2020, 6 (4) : 1236 - 1253
[2] Singular torsion points on elliptic curves
Boxall, J
Grant, D
MATHEMATICAL RESEARCH LETTERS, 2003, 10 (5-6) : 847 - 866
[3] Torsion points and reduction of elliptic curves
Yasuda, Masaya
ACTA ARITHMETICA, 2016, 176 (01) : 89 - 100
[4] Pair correlation of torsion points on elliptic curves
Alkan, Emre
Xiong, Maosheng
Zaharescu, Alexandru
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 356 (02) : 752 - 763
[5] The average number of torsion points on elliptic curves
Huang, Hsiu-Lien
JOURNAL OF NUMBER THEORY, 2014, 135 : 374 - 389
[6] Torsion points and matrices defining elliptic curves
Ravindra, G. V.
Tripathi, Amit
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2014, 24 (06) : 879 - 891
[7] Fields generated by torsion points of elliptic curves
Bandini, Andrea
Paladino, Laura
JOURNAL OF NUMBER THEORY, 2016, 169 : 103 - 133
[8] Elliptic curves with large intersection of projective torsion points
Bogomolov, Fedor A.
Fu, Hang
EUROPEAN JOURNAL OF MATHEMATICS, 2018, 4 (02) : 555 - 560
[9] TORSION POINTS AND GALOIS REPRESENTATIONS ON CM ELLIPTIC CURVES
Bourdon, Abbey
Clark, Pete L.
PACIFIC JOURNAL OF MATHEMATICS, 2020, 305 (01) : 43 - 88
[10] ON TORSION POINTS OF CERTAIN CM ELLIPTIC CURVES
Murabayashi, Naoki
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2012, 47 (01) : 89 - 93

← 1 2 3 4 5 →