Efficient Solution of Rational Conics
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.
| Main Authors: | , |
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| Format: | Article |
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American Mathematical Society
2001
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| Online Access: | https://eprints.nottingham.ac.uk/60/ |
| _version_ | 1848790363709374464 |
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| author | Cremona, John E Rusin, David |
| author_facet | Cremona, John E Rusin, David |
| author_sort | Cremona, John E |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:11:26Z |
| format | Article |
| id | nottingham-60 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:11:26Z |
| publishDate | 2001 |
| publisher | American Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-602020-05-04T20:32:42Z https://eprints.nottingham.ac.uk/60/ Efficient Solution of Rational Conics Cremona, John E Rusin, David 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. American Mathematical Society 2001 Article PeerReviewed Cremona, John E and Rusin, David (2001) Efficient Solution of Rational Conics. Mathematics of Computation . (In Press) genus one curves conics rational points |
| spellingShingle | genus one curves conics rational points Cremona, John E Rusin, David Efficient Solution of Rational Conics |
| title | Efficient Solution of Rational Conics |
| title_full | Efficient Solution of Rational Conics |
| title_fullStr | Efficient Solution of Rational Conics |
| title_full_unstemmed | Efficient Solution of Rational Conics |
| title_short | Efficient Solution of Rational Conics |
| title_sort | efficient solution of rational conics |
| topic | genus one curves conics rational points |
| url | https://eprints.nottingham.ac.uk/60/ |