engleski

Elliptic curves induced by Diophantine triples

Given a Diophantine triple {; ; ; ; ; ; ; ; ; c1(t), c2(t), c3(t)}; ; ; ; ; ; ; ; ; , the elliptic curve over Q(t) induced by this triple, i.e. y^2 = (c1(t)x+1) (c2(t)x+1)(c3(t)x+1), can have as torsion group one of the non-cyclic groups in Mazur's theorem, i.e. Z/2Z x Z/2Z, Z/2Z x Z/4Z, Z/2Z x Z/6Z or Z/2Z x Z/8Z. In this paper we present results concerning the rank over Q(t) of these curves improving in some of the cases the previously known results.

Elliptic curves, Diophantine triples, rank, torsion group

nije evidentirano