Table of Contents
Journal of Numbers
Volume 2014 (2014), Article ID 825634, 5 pages
http://dx.doi.org/10.1155/2014/825634
Research Article

On the Equation

1Adobe Research India Lab, Bangalore, Karnataka, India
2Department of Computer Science, University of Southern California, Los Angeles, CA 90089-0781, USA

Received 4 May 2014; Accepted 1 July 2014; Published 16 July 2014

Academic Editor: Cheon S. Ryoo

Copyright © 2014 Iftikhar A. Burhanuddin and Ming-Deh A. Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider certain quartic twists of an elliptic curve. We establish the rank of these curves under the Birch and Swinnerton-Dyer conjecture and obtain bounds on the size of Shafarevich-Tate group of these curves. We also establish a reduction between the problem of factoring integers of a certain form and the problem of computing rational points on these twists.