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Visualising 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-Swinnerton-Dyer 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 threefold.


Visualising elements of order 7 in the Tate-Shafarevich group of an elliptic curve   (20 pages)     dvi   ps   ps.gz   pdf

Plain text versions of the tables, and a Magma file checking some of the calculations in the paper are available here and here. These files have been updated to include the 2-parts of the conductors of the genus 2 Jacobians, computed in September 2017 by T. Dokchitser and C. Doris as described here.