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   * Birch's [[attachment:Birch-Conjectures_Concerning_Elliptic_Curves.pdf|article that introduces the Birch and Swinnerton-Dyer Conjecture]]
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   * Computing tables of elliptic curves over the field $\mathbf{Q}(\sqrt{5})$, e.g., as described [[http://wstein.org/talks/2011-02-11-sqrt5/|in this talk]], along with extensive data related to the Birch and Swinnerton-Dyer conjecture about each curve. This will involve both theoretical work and coding projects.    * '''Main topic''': Creating tables of elliptic curves over the field $\mathbf{Q}({\rm sqrt}{5})$, e.g., as described [[http://wstein.org/talks/2011-02-11-sqrt5/|in this talk]], along with extensive data related to the Birch and Swinnerton-Dyer conjecture about each curve, and investigating related conjectures. This will involve both theoretical work and coding projects.
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   * Helping John Cremona to extend his [[http://www.warwick.ac.uk/~masgaj/ftp/data/|highly influential tables]].

2011 Mathematics REU at UW

June 20 - August 12, 2011

Elliptic Curves

The elliptic curves REU will consist of projects involving elliptic curves, modular forms, and databases, and make extensive use of Sage. It will be organized by William Stein, and the number theory postdoc Jon Bober and grad students Alyson Deines and Simon Spicer will also likely help out. There will be about 6 students.

Pre-REU Reading List

Topics may include

  • Main topic: Creating tables of elliptic curves over the field \mathbf{Q}({\rm sqrt}{5}), e.g., as described in this talk, along with extensive data related to the Birch and Swinnerton-Dyer conjecture about each curve, and investigating related conjectures. This will involve both theoretical work and coding projects.

  • Computing additional data about elliptic curves over \mathbf{Q}, thus extending the data in http://db.modform.org/

  • Computing tables of modular forms (see my book).

reu/2011 (last edited 2011-07-07 21:34:26 by was)