engleski

On the rank of elliptic curves coming from rational Diophantine triples

We construct a family of Diophantine triples {; ; ; ; ; ; c_1(t), c_2(t), c_3(t)}; ; ; ; ; ; such that the elliptic curve over Q(t) induced by this triple, i.e.: y2 = (c_1(t) x + 1)(c_2(t) x + 1)(c_3(t) x + 1) has torsion group isomorphic to Z/2Z * Z/2Z and rank 5. This represents an improvement of the result of A. Dujella, who showed a family of this kind with rank 4. By specialization we obtain two examples of elliptic curves over Q with torsion group Z/2Z * Z/2Z and rank equal to 11. This is also an improvement over the known results relating this kind of curves.

elliptic curves; rank; Diophantine triples

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