engleski

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

The problem of extendibility of Diophantine triples in Q is closely connected with the properties of elliptic curves induced by them. The possible torsion groups of elliptic curves induced by Diophantine triples over quadratic fields, which do not appear over Q, are Z/2Z × Z/10Z, Z/2Z × Z/12Z and Z/4Z × Z/4Z. We showed that all these torsion groups indeed appear over some quadratic field. Moreover, we proved that there are infinitely many Diophantine triples over quadratic fields which induce elliptic curves with these torsion groups. This is joint work with Andrej Dujella and Ivan Soldo.

elliptic curve ; quadratic field ; torsion group ; Diophantine triple

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