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

#### Ahmed El Amine YOUMBAI [1] , A. Muhammed ULUDAĞ [2] , Djilali BEHLOUL [3]

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).
Elliptic Curves, Rank, Rational Cuboid, Diophantine Triples
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-3641-1800Author: Ahmed El Amine YOUMBAI (Primary Author)Institution: USTHBCountry: Algeria Orcid: 0000-0001-7761-8472Author: A. Muhammed ULUDAĞInstitution: GALATASARAY UNIVERSITYCountry: Turkey Orcid: 0000-0003-4631-5529Author: Djilali BEHLOULInstitution: USTHBCountry: Algeria Publication Date : June 7, 2021
 Bibtex @research article { hujms708945, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {721 - 731}, doi = {10.15672/hujms.708945}, title = {Elliptic curve involving subfamilies of rank at least 5 over \$\\mathbb\{Q\}(t)\$ or \$\\mathbb\{Q\}(t,k)\$}, key = {cite}, author = {Youmbaı, Ahmed El Amine and Uludağ, A. Muhammed and Behloul, Djilali} } APA Youmbaı, A , Uludağ, A , Behloul, D . (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 . DOI: 10.15672/hujms.708945 MLA Youmbaı, A , Uludağ, A , Behloul, D . "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 (2021 ): 721-731 Chicago Youmbaı, A , Uludağ, A , Behloul, D . "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 (2021 ): 721-731 RIS TY - JOUR T1 - Elliptic curve involving subfamilies of rank at least 5 over $\mathbb{Q}(t)$ or $\mathbb{Q}(t,k)$ AU - Ahmed El Amine Youmbaı , A. Muhammed Uludağ , Djilali Behloul Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.708945 DO - 10.15672/hujms.708945 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 721 EP - 731 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.708945 UR - https://doi.org/10.15672/hujms.708945 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Elliptic curve involving subfamilies of rank at least 5 over $\mathbb{Q}(t)$ or $\mathbb{Q}(t,k)$ %A Ahmed El Amine Youmbaı , A. Muhammed Uludağ , Djilali Behloul %T Elliptic curve involving subfamilies of rank at least 5 over $\mathbb{Q}(t)$ or $\mathbb{Q}(t,k)$ %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.708945 %U 10.15672/hujms.708945 ISNAD Youmbaı, Ahmed El Amine , Uludağ, A. Muhammed , Behloul, Djilali . "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 (June 2021): 721-731 . https://doi.org/10.15672/hujms.708945 AMA Youmbaı A , Uludağ A , Behloul D . 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. Vancouver Youmbaı A , Uludağ A , Behloul D . 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. IEEE A. Youmbaı , A. Uludağ and D. 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, pp. 721-731, Jun. 2021, doi:10.15672/hujms.708945

Authors of the Article
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