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)
JournalEuropean Journal of Mathematics
Publication statusAccepted/In press - Jan 1 2019



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

ASJC Scopus subject areas

  • Mathematics(all)

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