Efficient Solution of Rational Conics

Cremona, John E; Rusin, David

Abstract

We present efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions. Unlike existing algorithms, no integer factorization is required, provided that the prime factors of the discriminant are known.

Citation

Cremona, J. E., & Rusin, D. (2003). Efficient Solution of Rational Conics. Mathematics of Computation, 72(243), 1417-1441. https://doi.org/10.1090/S0025-5718-02-01480-1

• Journal Article Type: Article
• Online Publication Date: Dec 18, 2002
• Publication Date: 2003
• Deposit Date: Apr 4, 2002
• Publicly Available Date: Oct 9, 2007
• Journal: Mathematics of Computation
• Print ISSN: 0025-5718
• Electronic ISSN: 1088-6842
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 72
• Issue: 243
• Pages: 1417-1441
• DOI: https://doi.org/10.1090/S0025-5718-02-01480-1
• Keywords: genus one curves, conics, rational points
• Public URL: https://nottingham-repository.worktribe.com/output/1023265
• Publisher URL: https://www.ams.org/journals/mcom/2003-72-243/S0025-5718-02-01480-1/home.html