Explicit Classification for Torsion Subgroups of Rational Points of Elliptic Curves

<正> We study the classification of elliptic curves E over the rationals Q according to the torsionsubgroups Etors(Q). More precisely, we classify those elliptic curves with Etors(Q) being cyclic witheven orders. We also give explicit formulas for generators of Etors(Q). These results, together withthe recent results of K. Ono for the non-cyclic Etors(Q), completely solve the problem of the explicitclassification and parameterization when E has a rational point of order 2.

Project supported by the National Natural Science Foundation of China (Grant No. 19771052);


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