Naslov
High rank elliptic curves induced by rational Diophantine triples

Autori
Dujella, Andrej ; Peral, Juan Carlos

Izvornik
Glasnik matematički (0017-095X) 55 (2020), 2; 237-252

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Elliptic curves, Diophantine triples, rank

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 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 ≥ 7, which are both the current records for that kind of curves.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA