TY  - JOUR
TI  - Elliptic curve involving subfamilies of rank at least 5 over $mathbb{Q}(t)$ or $mathbb{Q}(t,k)$
AB  - 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).
AU  - Uludag, Muhammed
AU  - djilali, behloul
AU  - Youmbai, Ahmed El Amine
DO  - 10.15672/hujms.708945
PY  - 2021
JO  - Hacettepe Journal of Mathematics and Statistics
VL  - 50
IS  - 3
SN  - 1303-5010
SP  - 721
EP  - 731
DB  - TRDizin
UR  - http://search/yayin/detay/494733
ER  -