Explicit classification for torsion subgroups of rational points of elliptic curves

Details Explicit classification for torsion subgroups of rational points of elliptic curves Explicit classification for torsion subgroups of rational points of elliptic curves

1998-09-03

arxiv.org/abs/math/9809207v1

Mathematics

Number Theory

Scientific paper

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.

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