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

Uludag, Muhammed; djilali, behloul; Youmbai, Ahmed El Amine

doi:10.15672/hujms.708945

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

Ahmed El Amine YOUMBAI, (LATN Laboratory, Faculty of Mathematics, USTHB, BP 32, El Alia, 16111 Bab Ezzouar, Algiers, Algeria)

A. Muhammed ULUDAĞ, (Galatasaray Üniversitesi, Matematik Bölümü, Çırağan Cad. 36, 34357 Beşiktaş, İstanbul, Türkiye)

Djilali Behloul (Computer Science Department, USTHB, BP 32, El Alia, 16111 Bab Ezzouar, Algiers, Algeria)

Hacettepe Journal of Mathematics and Statistics

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Yıl: 2021 Cilt: 50 Sayı: 3 Sayfa Aralığı: 721 - 731 Metin Dili: İngilizce DOI: 10.15672/hujms.708945 İndeks Tarihi: 29-07-2022

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

Öz:

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

Anahtar Kelime: Diophantine Triples Elliptic Curves Rational Cuboid Rank

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	Youmbai A, Uludag M, djilali b (2021). Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. , 721 - 731. 10.15672/hujms.708945
Chicago	Youmbai Ahmed El Amine,Uludag Muhammed,djilali behloul Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. (2021): 721 - 731. 10.15672/hujms.708945
MLA	Youmbai Ahmed El Amine,Uludag Muhammed,djilali behloul Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. , 2021, ss.721 - 731. 10.15672/hujms.708945
AMA	Youmbai A,Uludag M,djilali b Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. . 2021; 721 - 731. 10.15672/hujms.708945
Vancouver	Youmbai A,Uludag M,djilali b Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. . 2021; 721 - 731. 10.15672/hujms.708945
IEEE	Youmbai A,Uludag M,djilali b "Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$." , ss.721 - 731, 2021. 10.15672/hujms.708945
ISNAD	Youmbai, Ahmed El Amine vd. "Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$". (2021), 721-731. https://doi.org/10.15672/hujms.708945

APA	Youmbai A, Uludag M, djilali b (2021). Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. Hacettepe Journal of Mathematics and Statistics, 50(3), 721 - 731. 10.15672/hujms.708945
Chicago	Youmbai Ahmed El Amine,Uludag Muhammed,djilali behloul Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. Hacettepe Journal of Mathematics and Statistics 50, no.3 (2021): 721 - 731. 10.15672/hujms.708945
MLA	Youmbai Ahmed El Amine,Uludag Muhammed,djilali behloul Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. Hacettepe Journal of Mathematics and Statistics, vol.50, no.3, 2021, ss.721 - 731. 10.15672/hujms.708945
AMA	Youmbai A,Uludag M,djilali b Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 721 - 731. 10.15672/hujms.708945
Vancouver	Youmbai A,Uludag M,djilali b Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 721 - 731. 10.15672/hujms.708945
IEEE	Youmbai A,Uludag M,djilali b "Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$." Hacettepe Journal of Mathematics and Statistics, 50, ss.721 - 731, 2021. 10.15672/hujms.708945
ISNAD	Youmbai, Ahmed El Amine vd. "Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$". Hacettepe Journal of Mathematics and Statistics 50/3 (2021), 721-731. https://doi.org/10.15672/hujms.708945