Naslov
High-rank elliptic curves induced by Diophantine triples

Autori
Dujella, Andrej ; Peral, Juan Carlos

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
29th Journées Arithmétiques / - Deberecen, 2015, 38-38

Skup
29th Journées Arithmétiques

Mjesto i datum
Debrecen, Mađarska, 06.07.2015. - 10.07.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
eloiptičke krivulje ; Diofantove trojke ; rang ; torzijska grupa
(elliptic curves ; Diophantine triples ; rank ; torsion group)

Sažetak
We study the possible structure of the groups of rational points on elliptic curves of the form y^2 = (x + ab)(x + ac)(x + bc), where a, b, c are non-zero rationals such that the product of any two of them is one less than a square. There are exactly four types of possible torsion groups for elliptic curves of this form. In each case, we construct examples and parametric families of elliptic curves with relatively high rank. In particular, we describe recent joint work with Juan Carlos Peral, with construction of an elliptic curve over the field of rational functions Q(t) with torsion group Z/2Z x Z/4Z and generic rank equal to 4, and an elliptic curve over Q with the same torsion group and rank 9. Both results improve previous records for ranks of curves with this torsion group.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA