Abstract
We prove the following.Theorem. Let be a number field, and the Jacobian of the curve parametrizing the elliptic curves with distinguished cyclic subgroups of order . If the number is written as , where contains a -simple abelian subvariety such that {\operatorname{rk}} A_k,$ SRC=http://ej.iop.org/images/0025-5734/11/2/A12/tex_sm_2058_img8.gif/> then the set of -isomorphism classes of elliptic curves over the field possessing -points of order is finite.Bibliography: 4 items.
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