### Abstract

Let E be an elliptic curve and π: E→ P^{1} 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) |
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Journal | European Journal of Mathematics |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

}

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 -