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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)
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.