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The projects in this proposal would generalize the highly influential
tables of Cremona to the next totally real number field and to higher
dimensional modular abelian varieties. This would improve on
algorithms available for computing with elliptic curves and abelian
varieties, and provide useful data and tools for number theory
researchers. The proposed research would also advance techniques for
constructing points and cohomology classes on elliptic curves, and for
understanding the arithmetic of elliptic curves over number fields.
This project would have as a concrete deliverable new publicly
available tables and software that will be of use to many number
theorists.
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