Explicit Classification for Torsion Subgroups of Rational Points of Elliptic Curves, by Derong Qiu and Xianke Zhang

The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classification are given when E_{tors}(Q) are cyclic groups with even orders. The generator points P of E_{tors}(Q) are also explicitly presented in each case. These results, together with recent results of K. Ono, completely solve the problem of the mentioned explicit classification when E has a rational point of order 2.

Derong Qiu and Xianke Zhang <xianke@tsinghua.edu.cn>