Explicit classification for torsion cyclic subgroups of rational points with event orders of elliptic curves

摘要

For elliptic curves E over rationals Q, the classification according to their torsion subgroups E_tors(Q)of rational points has been studied. When E_tors(Q)are cyclic groups with even orders, the classification is given with explicit criteria, and the generators of the torsion groups are also explicitly presented in each case. These results, together with the recent re- sults of Ono for the non-cyclic torsion groups, have completely solved the problem of the explicit classification with E being rational point of order 2.