# Deciding Existence of Rational Points on Curves: An Experiment

@article{Bruin2008DecidingEO, title={Deciding Existence of Rational Points on Curves: An Experiment}, author={Nils Bruin and Michael Stoll}, journal={Experimental Mathematics}, year={2008}, volume={17}, pages={181 - 189} }

In this paper we gather experimental evidence related to the question of deciding whether a curve has a rational point. We consider all genus-2 curves over ℚ given by an equation y 2 = f(x) with f a square-free polynomial of degree 5 or 6, with integral coefficients of absolute value at most 3. For each of these roughly 200 000 isomorphism classes of curves, we decide whether there is a rational point on the curve by a combination of techniques that are applicable to hyperelliptic curves in… Expand

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