Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage.
We give an overview of some p-adic algorithms for computing with el-liptic and hyperelliptic curves, starting with Kedlaya's algorithm. While the original purpose of Kedlaya's algorithm was to compute the zeta function of a hyperel-liptic curve over a finite field, it has since been used in a number of applications. In particular, we describe how to use… (More)
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 and thereby compute Heegner points of non-fundamental discriminant. We then prove a relationship between the… (More)