engleski

On the Mordell-Weil group of elliptic curves induced by the families of Diophantine triples

The problem of the extendibility of Diophantine triples is closely connected with the Mordell-Weil group of the associated elliptic curve. In this paper, we examine Diophantine triples {; ; k−1, k+1, c_l(k)}; ; and prove that the torsion group of the associated curves is ℤ/2ℤ×ℤ/2ℤ for l=3, 4 and l≡1 or 2(mod4). Additionally, we prove that the rank is greater than or equal to 2 for all l≥2. This represents an improvement of previous results by Dujella, Petho and Najman, where cases k=2 and l≤3 were considered.

Diophantine triples; elliptic curves; Mordell-Weil group

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