Explicit classification for torsion subgroups of rational points of elliptic curves

Derong Qiu; Xianke Zhang

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Explicit classification for torsion subgroups of rational points of elliptic curves

Derong Qiu·Xianke Zhang

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Abstract

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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BibTeX RIS

Derong Qiu, Xianke Zhang. 1998-09-03. Explicit classification for torsion subgroups of rational points of elliptic curves. https://arxiv.org/abs/math/9809207

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