2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171991We 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.12 pagesNumber Theory11D41, 11G30, 11Y50 (Primary) 14G05, 14G25, 14H25, 14H45, 14Q05 (Secondary)text