Deciding existence of rational points on curves: an experiment
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2006
 arXiv:
 arXiv:math/0604524
 Bibcode:
 2006math......4524B
 Keywords:

 Mathematics  Number Theory;
 11D41;
 11G30;
 11Y50 (Primary) 14G05;
 14G25;
 14H25;
 14H45;
 14Q05 (Secondary)
 EPrint:
 12 pages