Visualizing elements of order two in the Weil–Châtelet group
نویسندگان
چکیده
منابع مشابه
Visualizing elements of order three in the Shafarevich-Tate group
1. Introduction. If we wish to write the equations of curves of genus 1 that give elements of the Shafarevich-Tate group of an elliptic curve over a number field K, a choice of ways is open to us. For example, if the element in question is of order 3 the curve of genus 1 corresponding to it occurs as a smooth plane cubic curve over K. In a recent article [C-M] we raised the question of when one...
متن کاملVisualizing Elements in the Shafarevich - Tate Group
As is well known, E(K) and X(E/K) are somehow linked in the sense that it is often easier to come by information about the Selmer group of E over K which is built out of both E(K) and X(E/K) than it is to get information about either of these groups separately. It occurred to us that, although these two groups (Mordell-Weil and X) are partners, so to speak, in the arithmetic analysis of the ell...
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چکیده ندارد.
15 صفحه اولVisualizing elements of order 7 in the Tate–Shafarevich group of an elliptic curve
We study the elliptic curves in Cremona’s tables that are predicted by the Birch–SwinnertonDyer conjecture to have elements of order 7 in their Tate–Shafarevich group. We show that in many cases these elements are visible in an abelian surface or abelian 3-fold.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2005
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.07.017