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Results and conjectures concerning orders of Tate-Shafarevich groups in families of elliptic curves

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Speaker: 
Andrzej Dabrowski
Affiliation: 
University of Szczecin
Date: 
Wed, 2019-05-22 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We plan to discuss numerical results and conjectures concerning orders of Tate-Shafarevich groups in
families of quadratic twists of elliptic curves, families of elliptic curves of Neumann-Setzer type and
families of cubic twists of X_0(27). We will give examples of elliptic curves with exceptionally large
orders of Tate-Shafarevich groups. We also calculate hypothetical orders of Tate-Shafarevich groups
for some quadratic twists of Gross curves. This is a joint work with Tomasz Jedrzejak and Lucjan
Szymaszkiewicz.

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