SELF-POINTS ON ELLIPTIC CURVES OF PRIME CONDUCTOR

Let E be an elliptic curve of conductor p. Given a cyclic subgroup C of order p in E[p], we construct a modular point P-C on E, called self-point, as the image of (E, C) on X-0(p) under the modular parametrization X0(p) -> E. We prove that the point is of infinite order in the Mordell-Weil group of E over the field of definition of C. One can deduce a lower bound on the growth of the rank of the Mordell-Weil group in its PGL(2)(Z(p))-tower inside Q(E[p(infinity)]).