Elliptic curve involving subfamilies of rank at least 5 over Q(t) or Q(t, k)

Creative Commons License

Youmbai A. E. A., Uludag M., Behloul D.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.50, sa.3, ss.721-731, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15672/hujms.708945
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.721-731
  • Anahtar Kelimeler: elliptic curves, rank, rational cuboid, diophantine triples, EQUAL-TO 5, EXAMPLE, FAMILY
  • Galatasaray Üniversitesi Adresli: Evet

Özet

Motivated by the work of Zargar and Zamani, we introduce a family of elliptic curves containing several one-(respectively two-) parameter subfamilies of high rank over the function field Q(t) (respectively Q(t, k)). Following the approach of Moody, we construct two subfamilies of infinitely many elliptic curves of rank at least 5 over Q(t, k). Secondly, we deduce two other subfamilies of this family, induced by the edges of a rational cuboid containing five independent Q(t)-rational points. Finally, we give a new subfamily induced by Diophantine triples with rank at least 5 over Q(t). By specialization, we obtain some specific examples of elliptic curves over Q with a high rank (8, 9, 10 and 11).