Deciding existence of rational points on curves: an experiment
| dc.creator | Bruin, Nils | |
| dc.creator | Stoll, Michael | |
| dc.date | 2006-04-25 | |
| dc.date.accessioned | 2026-07-07T10:11:51Z | |
| dc.date.available | 2026-07-07T10:11:51Z | |
| dc.description | 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. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604524 | |
| dc.identifier | http://arxiv.org/abs/math/0604524 | |
| dc.identifier | Experiment. Math. 17 (2008), no. 2, 181--189. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171991 | |
| dc.subject | Number Theory | |
| dc.subject | 11D41, 11G30, 11Y50 (Primary) 14G05, 14G25, 14H25, 14H45, 14Q05 (Secondary) | |
| dc.title | Deciding existence of rational points on curves: an experiment | |
| dc.type | text |