engleski

Construction of high rank elliptic curves

We list a number of strategies for construction of elliptic curves having high rank with special emphasis on those curves induced by Diophantine triples, in which we have contributedmore. These strategies have been developed by many authors. In particular we present a new example of a curve, induced by a Diophantine triple, with torsion Z/2Z × Z/4Z and with rank 9 over Q. This is the present record for this kind of curves.

Elliptic curves, rank, torsion group, Diophantine triples

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