On the PGL 2 -invariant quadruples of torsion points of elliptic curves

Research output: Contribution to journalArticle

Abstract

Let E be an elliptic curve and π: E→ P1 a standard double cover identifying ±P∈E. It is known that for some torsion points Pi∈ E, 1 ⩽ i⩽ 4 , the cross ratio of {π(Pi)}i=14 is independent of E. We will give a complete classification of such quadruples.

Original languageEnglish (US)
JournalEuropean Journal of Mathematics
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Torsion Points
Quadruple
Pi
Elliptic Curves
Cross ratio
Invariant
Cover
Standards

Keywords

  • Congruence subgroups
  • Elliptic curves
  • Modular curves
  • q-series
  • Torsion points

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the PGL 2 -invariant quadruples of torsion points of elliptic curves. / Bogomolov, Fedor A.; Fu, Hang.

In: European Journal of Mathematics, 01.01.2019.

Research output: Contribution to journalArticle

@article{99c0e60e68af4d549374c8102d6760dc,
title = "On the PGL 2 -invariant quadruples of torsion points of elliptic curves",
abstract = "Let E be an elliptic curve and π: E→ P1 a standard double cover identifying ±P∈E. It is known that for some torsion points Pi∈ E, 1 ⩽ i⩽ 4 , the cross ratio of {π(Pi)}i=14 is independent of E. We will give a complete classification of such quadruples.",
keywords = "Congruence subgroups, Elliptic curves, Modular curves, q-series, Torsion points",
author = "Bogomolov, {Fedor A.} and Hang Fu",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s40879-019-00377-w",
language = "English (US)",
journal = "European Journal of Mathematics",
issn = "2199-675X",
publisher = "Springer International Publishing AG",

}

TY - JOUR

T1 - On the PGL 2 -invariant quadruples of torsion points of elliptic curves

AU - Bogomolov, Fedor A.

AU - Fu, Hang

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Let E be an elliptic curve and π: E→ P1 a standard double cover identifying ±P∈E. It is known that for some torsion points Pi∈ E, 1 ⩽ i⩽ 4 , the cross ratio of {π(Pi)}i=14 is independent of E. We will give a complete classification of such quadruples.

AB - Let E be an elliptic curve and π: E→ P1 a standard double cover identifying ±P∈E. It is known that for some torsion points Pi∈ E, 1 ⩽ i⩽ 4 , the cross ratio of {π(Pi)}i=14 is independent of E. We will give a complete classification of such quadruples.

KW - Congruence subgroups

KW - Elliptic curves

KW - Modular curves

KW - q-series

KW - Torsion points

UR - http://www.scopus.com/inward/record.url?scp=85074573178&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074573178&partnerID=8YFLogxK

U2 - 10.1007/s40879-019-00377-w

DO - 10.1007/s40879-019-00377-w

M3 - Article

AN - SCOPUS:85074573178

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

ER -