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Darrin Doud

214 TMCB Department of Mathematics Brigham Young University Provo, UT 84602

phone: (801)422-1204 fax: (801)422-0504 e-mail:

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A procedure to calculate torsion of elliptic curves over Q

Manuscripta Mathematica, 95 (1998), pp. 463-469.

Abstract We present an algorithm which uses the analytic parameterization of elliptic curves to rapidly calculate torsion subgroups, and calculate its running time. This algorithm is much faster than the "traditional" Lutz-Nagell algorithm used by most computer algebra systems to calculate torsion subgroups.

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Cited By

• Irene Garcia-Selfa, Miguel A. Olalla, and Jose M. Tornero, Computing the rational torsion of an elliptic curve using Tate normal form, J. Number Theory 96 (2002), no. 1, 76--88.
• GP/PARI Source Code, http://pari.math.u-bordeaux.fr/.
• Iftikhar A. Burhanuddin and Ming-Deh A. Huang, Elliptic curve torsion points and division polynomials, Computational Aspects of Algebraic Curves, T. Shaska (Ed.), Lecture Notes Series on Computing, 13 (2005), 13--37, World Scientific/
• Susanne Schmitt and Horst G. Zimmer, Elliptic Curves: A Computational Approach, de Gruyter Studies in Mathematics, 31. Walter de Gruyter \& Co., Berlin, 2003.
• Iftikhar A. Burhanuddin, Some computational problems motivated by the Birch and Swinnerton-Dyer conjecture, Ph.D. Thesis, University of Southern California, Department of Computer Science, 2007.
• Bryan Faulkner, Estimates related to the arithmetic of elliptic curves, Ph.D. Thesis, Clemson University, 2007.
• Lawrence Washington, Elliptic Curves, Number Theory and Cryptography, Second Edition, Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2008.
• Enrique Gonzalez-Jimenez and Jose M. Tornero, On the ubiquity of trivial torsion on elliptic curves, Arch. Math. (Basel), 95 (2010), 135-141.
• Alvaro Lozano-Robledo, Elliptic Curves, Modular Forms, and their L-functions, American Mathematical Society, 2011.
• Władysław Narkievicz, Rational Number Theory in the 20th century. From PNT to FLT., Springer Monographs in Mathematics, Springer, London, 2012.