On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields

Abstract

The possible torsion groups of elliptic curves induced by Diophantine triples over quadratic fields, which do not appear over Q, are Z/2Z x Z/10Z, Z/2Z x Z/12Z and Z/4Z x Z/4Z. In this paper, we show that all these torsion groups indeed appear over some quadratic field. Moreover, we prove that there are infinitely many Diophantine triples over quadratic fields which induce elliptic curves with these torsion groups.

arXiv comment13 pages

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Cited by in corpus (3)

• Elliptic curves induced by Diophantine triples
• Elliptic curves with torsion groups $\mathbb{Z}/8\mathbb{Z}$ and $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/6\mathbb{Z}$
• On elliptic curves induced by rational Diophantine quadruples