Number Theory Seminar

Tuesday 16 January 2007, MR13, 2:30pm

Self-points on elliptic curves
Christian Wuthrich (Lausanne)


     Let E be an elliptic curve of conductor N. Given a cyclic subgroup C of order N in E, we construct a modular point P_C on E, called self-point, as the image of (E,C) on X_0(N) under the modular parametrisation X_0(N)->E. If N=p is prime, we prove that the point is of infinite order in the Mordell-Weil group of E over the field of definition of C. The study of these points in the PGL_2(Z_p)-tower inside Q(E[p^infty]) continue earlier work of Harris.

Last modified on 20/1/07.

Comments/corrections to Tim Dokchitser