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

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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)
Pages (from-to)1236-1253
Number of pages18
JournalEuropean Journal of Mathematics
Issue number4
StatePublished - Dec 2020


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

ASJC Scopus subject areas

  • Mathematics(all)


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