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Elliptic Curves of High Rank with Nontrivial Torsion Group over Q

Elliptic Curves of High Rank with Nontrivial Torsion Group over Q

We construct elliptic curves over Q of high Mordell-Weil rank, with a nontrivial torsion subgroup. We improve the rank records for the cases Z/2Z × Z/2Z, Z/3Z, Z/4Z, Z/5Z, Z/6Z, Z/7Z and Z/8Z.