Elliptic curves induced by Diophantine triples
Abstract
Given a Diophantine triple \c1(t),c2(t),c3(t)\, the elliptic curve over Q(t) induced by this triple, i.e. y2=(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.
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