On elliptic curves induced by rational Diophantine quadruples


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Dujella A., SOYDAN G.

Proceedings of the Japan Academy Series A: Mathematical Sciences, vol.98, no.1, 2022 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 98 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.3792/pjaa.98.001
  • Title of Journal : Proceedings of the Japan Academy Series A: Mathematical Sciences
  • Keywords: Diophantine quadruples, Elliptic curves, Rank, Torsion group

Abstract

© 2022. The Japan AcademyIn this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four non-zero rationals such that the product of any two of them plus 1 is a perfect square. We show that for each of the groups Z/2Z × Z/kZ for k = 2, 4, 6, 8, there are infinitely many rational Diophantine quadruples with the property that the induced elliptic curve has this torsion group. We also construct curves with moderately large rank in each of these four cases