Sieving for rational points on hyperelliptic curves

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چکیده

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Sieving for rational points on hyperelliptic curves

We give a new and efficient method of sieving for rational points on hyperelliptic curves. This method is often successful in proving that a given hyperelliptic curve, suspected to have no rational points, does in fact have no rational points; we have often found this to be the case even when our curve has points over all localizations Qp. We illustrate the practicality of the method with some ...

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ژورنال

عنوان ژورنال: Mathematics of Computation

سال: 2001

ISSN: 0025-5718

DOI: 10.1090/s0025-5718-01-01275-3