Naslov
Mordell-Weil groups of elliptic curves induced by Diophantine triples

Autori
Dujella, Andrej

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

Izvornik
First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Number Theory Session / - , 2014, 3-3

Skup
First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI

Mjesto i datum
Bilbao, Španjolska, 30.06.2014. - 04.07.2014

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
elliptic curves ; torsion group ; rank ; Diophantine triples

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 nonzero rationals such that the product of any two of them is one less than a square. Such a triple {; ; a, b, c}; ; is called a rational Diophantine triple. 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 a 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