We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and methods based on quasiorthogonality in the Mordell-Weil lattice ([Sil6], [GS], [He]). We apply our results to break previous bounds on the number of elliptic curves of given conductor and the size of the 3-torsion part of the class group of a quadratic field. The same ideas can be used to count rational points on curves of higher genus.
|Translated title of the contribution||Integral points on elliptic curves and 3-torsion in class groups|
|Pages (from-to)||527 - 550|
|Number of pages||24|
|Journal||Journal of the American Mathematical Society|
|Publication status||Published - Jul 2006|
Bibliographical notePublisher: American Mathematical Society
Other identifier: IDS number 042FR