Tschirnhaus-Weierstrass curves

2008/08/22 by Josef Schicho, Schicho, Josef, David Sevilla +1
Computer Science · Engineering · Mathematics · #14H99 (Primary) 14Q05 #68W30 (Secondary) #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Edwards curve #Elliptic curve #FOS: Computer and information sciences #FOS: Mathematics #Geometry #Hessian form of an elliptic curve #Jacobian curve #Mathematics #Polynomial and algebraic computation #Pure mathematics #Representation (politics) #Scaling #Schoof's algorithm #Symbolic Computation (cs.SC) #Tripling-oriented Doche–Icart–Kohel curve #Weierstrass functions #cs.SC #math.AG #msc:14H99 #msc:14Q05 #msc:68W30

paper · pdf · doi:10.48550/arxiv.0808.3038

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

openalex publication_date 2008/08/22 · arxiv created 2011/06/09 · arxiv updated 2011/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Principles of Algebraic Geometry

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