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Deciding existence of rational points on curves: an experiment

Research paper by Nils Bruin, Michael Stoll

Indexed on: 25 Apr '06Published on: 25 Apr '06Published in: Mathematics - Number Theory



Abstract

We consider all genus 2 curves over Q given by an equation y^2 = f(x) with f a squarefree polynomial of degree 5 or 6, with integral coefficients of absolute value at most 3. For each of these roughly 200000 isomorphism classes of curves, we decide if there is a rational point on the curve or not, by a combination of techniques. For a small number of curves, our result is conditional on the BSD conjecture or on GRH.