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Visualizing elements of order $7$ in the Tate–Shafarevich group of an elliptic curve
Published online by Cambridge University Press: 26 August 2016
Abstract
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 3-fold.
MSC classification
- Type
- Research Article
- Information
- LMS Journal of Computation and Mathematics , Volume 19 , Special Issue A: Algorithmic Number Theory Symposium XII , 2016 , pp. 100 - 114
- Copyright
- © The Author 2016