### 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 | |

Publication status | Accepted/In press - Jan 1 2019 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)