The author must begin with an apology for writing on a topic so specific, so elementary, and so well-understood as the study of elliptic curves of rank 1. Nevertheless, it is hoped that a contribution not entirely without value or novelty is to be found within the theory of Selmer varieties for hyperbolic curves, applied to the complement X = E \ {e} of the origin inside an elliptic curve E over Q with Mordell-Weil rank 1. Assume throughout this paper that p is an odd prime of good reduction such that X(E)[p ∞ ] is finite and that E has integral j-invariant. All of these assumptions will hold, for example, if E has complex multiplication and ord s=1 L(E, s) = 1.Let E be a regular Z-model for E and X the complement in E of the closure of e. The main goal of the present inquiry is to find explicit analytic equations defining X (Z) inside X (Z p ). The approach of this paper makes use of a rigidified Massey product in Galois cohomology.1 That is, theétale local unipotent Albanese map2 ) to the level-two local Selmer variety (recalled below) associates to point z a nonabelian cocycle a(z), which can be broken canonically into two components a(z) = a 1 (z) + a 2 (z), with a 1 (z) taking values in to construct a function on the local points of X . Recall that Massey products are secondary cohomology products arising in connection with associative differential graded algebras (A,