# Glasnik matematički,Vol. 55 No. 2, 2020.

Izvorni znanstveni članak
https://doi.org/10.3336/gm.55.2.05

High rank elliptic curves induced by rational Diophantine triples

Andrej Dujella   orcid.org/0000-0001-6867-5811 ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Juan Carlos Peral ; Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain

 Puni tekst: engleski, pdf (157 KB) str. 237-252 preuzimanja: 115* citiraj APA 6th EditionDujella, A. i Peral, J.C. (2020). High rank elliptic curves induced by rational Diophantine triples. Glasnik matematički, 55 (2), 237-252. https://doi.org/10.3336/gm.55.2.05 MLA 8th EditionDujella, Andrej i Juan Carlos Peral. "High rank elliptic curves induced by rational Diophantine triples." Glasnik matematički, vol. 55, br. 2, 2020, str. 237-252. https://doi.org/10.3336/gm.55.2.05. Citirano 20.10.2021. Chicago 17th EditionDujella, Andrej i Juan Carlos Peral. "High rank elliptic curves induced by rational Diophantine triples." Glasnik matematički 55, br. 2 (2020): 237-252. https://doi.org/10.3336/gm.55.2.05 HarvardDujella, A., i Peral, J.C. (2020). 'High rank elliptic curves induced by rational Diophantine triples', Glasnik matematički, 55(2), str. 237-252. https://doi.org/10.3336/gm.55.2.05 VancouverDujella A, Peral JC. High rank elliptic curves induced by rational Diophantine triples. Glasnik matematički [Internet]. 2020 [pristupljeno 20.10.2021.];55(2):237-252. https://doi.org/10.3336/gm.55.2.05 IEEEA. Dujella i J.C. Peral, "High rank elliptic curves induced by rational Diophantine triples", Glasnik matematički, vol.55, br. 2, str. 237-252, 2020. [Online]. https://doi.org/10.3336/gm.55.2.05

Sažetak
A rational Diophantine triple is a set of three nonzero rational $a,b,c$ with the property that $ab+1$, $ac+1$, $bc+1$ are perfect squares. We say that the elliptic curve $y^2 = (ax+1)(bx+1)(cx+1)$ is induced by the triple $\{a,b,c\}$. In this paper, we describe a new method for construction of elliptic curves over $\mathbb{Q}$ with reasonably high rank based on a parametrization of rational Diophantine triples. In particular, we construct an elliptic curve induced by a rational Diophantine triple with rank equal to $12$, and an infinite family of such curves with rank $\geq 7$, which are both the current records for that kind of curves.

Ključne riječi
Elliptic curves; Diophantine triples; rank

Hrčak ID: 248665

Posjeta: 212 *