Explicit classification for torsion subgroups of rational points of elliptic curves
Derong Qiu, Xianke Zhang
Abstract
The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups Etors(Q) of rational points. Explicit criteria for the classification are given when Etors(Q) are cyclic groups with even orders. The generator points P of Etors(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.
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