Tschirnhaus-Weierstrass curves

Abstract

We define the concept of Tschirnhaus-Weierstrass curve, named after the Weierstrass form of an elliptic curve and Tschirnhaus transformations. Every pointed curve has a Tschirnhaus-Weierstrass form, and this representation is unique up to a scaling of variables. This is useful for computing isomorphisms between curves.

v2: 10 pages, major revision due to errors in the main result. v1: 14 pages, submitted to Mathematics of Computation