Finding suitable curves for the elliptic curve method of factorization

A. O. Atkin; F. Morain

doi:10.1090/S0025-5718-1993-1140645-1

Finding suitable curves for the elliptic curve method of factorization

A. O. Atkin
, F. Morain

University of Illinois at Chicago

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	399-405
Number of pages	7
Journal	Mathematics of Computation
Volume	60
Issue number	201
DOIs	https://doi.org/10.1090/S0025-5718-1993-1140645-1
Publication status	Published - 1 Jan 1993

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title = "Finding suitable curves for the elliptic curve method of factorization",

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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year = "1993",

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AU - Morain, F.

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84968494111

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DO - 10.1090/S0025-5718-1993-1140645-1

M3 - Article

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VL - 60

SP - 399

EP - 405

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 201

ER -

Finding suitable curves for the elliptic curve method of factorization

Abstract

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