An algorithm for finding a minimal Weierstrass equation for an elliptic curve

Abstract

Let <italic>E</italic> be an elliptic curve defined over an algebraic number field <italic>K</italic> and assume that some Weierstrass equation for <italic>E</italic> over <italic>K</italic> is given. Then an algorithm is described which yields a global minimal Weierstrass equation for <italic>E</italic> over <italic>K</italic> provided such a global minimal Weierstrass equation does exist.