Abstract
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 |
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Original language | English |
Pages (from-to) | 527 - 550 |
Number of pages | 24 |
Journal | Journal of the American Mathematical Society |
Volume | 19 (3) |
DOIs | |
Publication status | Published - Jul 2006 |
Bibliographical note
Publisher: American Mathematical SocietyOther identifier: IDS number 042FR