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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Tschirnhaus-Weierstrass curves


Authors: Josef Schicho and David Sevilla
Journal: Math. Comp.
MSC (2010): Primary 14H99; Secondary 14Q05, 68W30
Published electronically: January 30, 2014
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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.


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Additional Information

Josef Schicho
Affiliation: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria
Email: josef.schicho@oeaw.ac.at

David Sevilla
Affiliation: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria
Address at time of publication: Univ. de Extremadura, C. U. de Mérida, Av. Santa Teresa de Jornet 38, E-06800 Mérida (Badajoz), Spain
Email: sevillad@unex.es

DOI: http://dx.doi.org/10.1090/S0025-5718-2014-02801-9
PII: S 0025-5718(2014)02801-9
Received by editor(s): October 17, 2008
Received by editor(s) in revised form: February 9, 2013
Published electronically: January 30, 2014
Additional Notes: The first author was partially supported by the FWF (Austrian Science Fund) in the frame of project 18992.
The second author was partially supported by the Spanish MEC project MTM2007-67088 and the FWF project P22766-N18.
Article copyright: © Copyright 2014 American Mathematical Society