  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.
