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Finding suitable curves for the elliptic curve method of factorization


Authors: A. O. L. Atkin and F. Morain
Journal: Math. Comp. 60 (1993), 399-405
MSC: Primary 11Y05; Secondary 11G20
DOI: https://doi.org/10.1090/S0025-5718-1993-1140645-1
MathSciNet review: 1140645
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Abstract: Using the parametrizations of Kubert, we show how to produce infinite families of elliptic curves which have prescribed nontrivial torsion over Q and rank at least one. These curves can be used to speed up the ECM factorization algorithm of Lenstra. We also briefly discuss curves with complex multiplication in this context.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1140645-1
Article copyright: © Copyright 1993 American Mathematical Society

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