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

Ahmed El Amine YOUMBAI; A. Muhammed ULUDAĞ; Djilali BEHLOUL

doi:https://doi.org/10.15672/hujms.708945

Makale detayları

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

Yazarlar:

Ahmed El Amine YOUMBAI | A. Muhammed ULUDAĞ | Djilali BEHLOUL

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 3, pp.721-731

Belge Tipi:

Makale

Yayın Tarihi:

6/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000450641

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.708945

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)Q(t)\mathbb{Q}(t) (respectively Q(t,k)Q(t,k)\mathbb{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)Q(t,k)\mathbb{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)Q(t)\mathbb{Q}(t)-rational points. Finally, we give a new subfamily induced by Diophantine triples with rank at least 5 over Q(t)Q(t)\mathbb{Q}(t). By specialization, we obtain some specific examples of elliptic curves over QQ\mathbb{Q} with a high rank (8, 9, 10 and 11).

Makale detayları

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

Yazarlar: Ahmed El Amine YOUMBAI | A. Muhammed ULUDAĞ | Djilali BEHLOUL

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 3, pp.721-731

Belge Tipi: Makale

Yayın Tarihi: 6/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000450641

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/hujms.708945

Sayı

Yazarlar:

Ahmed El Amine YOUMBAI | A. Muhammed ULUDAĞ | Djilali BEHLOUL

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 3, pp.721-731

Belge Tipi:

Makale

Yayın Tarihi:

6/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000450641

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.708945