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, cilt.98, sa.1, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 98 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3792/pjaa.98.001
  • Dergi Adı: Proceedings of the Japan Academy Series A: Mathematical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Diophantine quadruples, elliptic curves, torsion group, rank, RANK, CONSTRUCTION, SEXTUPLES, Q(T)
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

© 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