Visualizing elements of order 7 in the Tate–Shafarevich group of an elliptic curve
نویسنده
چکیده
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.
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...
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