p-ADIC HEIGHTS OF HEEGNER POINTS AND ANTICYCLOTOMIC Λ-ADIC REGULATORS

Let E be an elliptic curve defined over Q. The aim of this paper is to make it possible to compute Heegner L-functions and anticyclotomic Λ-adic regulators of E, which were studied by Mazur-Rubin and Howard. We generalize results of Cohen and Watkins, which enable us to compute Heegner points of non-fundamental discriminant. We then prove a relationship between the denominator of a point of E defined over a number field and the leading coefficient of the minimal polynomial of its xcoordinate. Using this, we recast earlier work of Mazur, Stein, and Tate, which then allows us to produce effective algorithms to compute p-adic heights of points of E defined over number fields. These methods make it possible for us to give the first explicit examples of Heegner L-functions and anticyclotomic Λ-adic regulators.