Efficient solution of rational conics

Cremona, J.; Rusin, D.

doi:10.1090/S0025-5718-02-01480-1

Efficient solution of rational conics
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by J. E. Cremona and D. Rusin;

Math. Comp. 72 (2003), 1417-1441

DOI: https://doi.org/10.1090/S0025-5718-02-01480-1

Published electronically: December 18, 2002

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Abstract:

We present efficient algorithms for solving Legendre equations over $\mathbb Q$ (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.

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