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

Fedor A. Bogomolov; Hang Fu

doi:10.1007/s40879-019-00377-w

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

Fedor A. Bogomolov, Hang Fu

Mathematics

Research output: Contribution to journal › Article › peer-review

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 P_i∈ 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 language	English (US)
Pages (from-to)	1236-1253
Number of pages	18
Journal	European Journal of Mathematics
Volume	6
Issue number	4
DOIs	https://doi.org/10.1007/s40879-019-00377-w
State	Published - Dec 2020

Keywords

Congruence subgroups
Elliptic curves
Modular curves
Torsion points
q-series

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s40879-019-00377-w

Cite this

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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, Torsion points, q-series",

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KW - Modular curves

KW - Torsion points

KW - q-series

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