High-rank elliptic curves with torsion induced by Diophantine triples
High-rank elliptic curves with torsion induced by Diophantine triples
Abstract We construct an elliptic curve over the field of rational functions with torsion group $\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/4\mathbb{Z}$ and rank equal to four, and an elliptic curve over $\mathbb{Q}$ with the same torsion group and rank nine. Both results improve previous records for ranks of curves of this torsion group. They …