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

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1993-1140645-1
PII: S 0025-5718(1993)1140645-1
Article copyright: © Copyright 1993 American Mathematical Society