Deciding existence of rational points on curves: an experiment
Nils Bruin, Michael Stoll
Abstract
We consider all genus 2 curves over Q given by an equation y2 = 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.
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