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

For elliptic curves E over the rationals Q, the classification according to their torsion subgroups Etors(Q) of rational points has been studied. When Etors(Q) are cyclic groups with even orders, the classification is given with explicit critria, and the generators of the torsion groups are also explicitly presented in each case. These results, together with the recent re-

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