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Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves


Authors: Andrzej Dąbrowski and Lucjan Szymaszkiewicz
Journal: Math. Comp. 87 (2018), 1509-1522
MSC (2010): Primary 11G05, 11G40, 11Y50
DOI: https://doi.org/10.1090/mcom/3248
Published electronically: September 8, 2017
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Abstract: We present the results of our search for the orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves.


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Additional Information

Andrzej Dąbrowski
Affiliation: Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
Email: andrzej.dabrowski@usz.edu.pl, dabrowskiandrzej7@gmail.com

Lucjan Szymaszkiewicz
Affiliation: Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
Email: lucjansz@gmail.com

DOI: https://doi.org/10.1090/mcom/3248
Keywords: Elliptic curves, Tate-Shafarevich group, Cohen-Lenstra heuristics, distribution of central $L$-values
Received by editor(s): May 31, 2016
Received by editor(s) in revised form: November 12, 2016
Published electronically: September 8, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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