Weierstrass coefficients of the canonical lifting

Abstract

Given an ordinary elliptic curve [Formula: see text] over a field of characteristic [Formula: see text], there are functions [Formula: see text] and [Formula: see text] such that the curve [Formula: see text] where [Formula: see text] and [Formula: see text] is the canonical lifting of [Formula: see text]. Although these functions are not uniquely determined, we prove that they can be taken to be in [Formula: see text], defined for all ordinary elliptic curves of the given characteristic, and modular, with [Formula: see text] and [Formula: see text].