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Deciding existence of rational points on curves : an experiment

Title data

Bruin, Nils ; Stoll, Michael:
Deciding existence of rational points on curves : an experiment.
In: Experimental Mathematics. Vol. 17 (2008) Issue 2 . - pp. 181-189.
ISSN 1058-6458

Official URL: Volltext

Abstract in another language

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 general.
In order to carry out our project, we have improved and optimized some of these techniques. For 42 of the curves, our result is conditional on the Birch and Swinnerton-Dyer conjecture or on the generalized Riemann hypothesis.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Rational points; curves; solvability; local-to-global obstruction; descent
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 26 Jan 2015 12:05
Last Modified: 12 Feb 2015 10:27
URI: https://eref.uni-bayreuth.de/id/eprint/6015