Ranks of quadratic twists of elliptic curves (Please note change in time)

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• Tom Fisher (Cambridge) / Andrew Granville (UCL)
• Tuesday 13 October 2015, 14:45-15:45
• MR13.

If you have a question about this talk, please contact Jack Thorne.

We report on a large-scale project searching for congruent number elliptic curves of large rank. As a result of these investigations there are now 27 curves known of rank 7, but none of rank 8. The methods used to exclude candidate curves include higher descents, and bounds on the analytic rank. We explain a heuristic (of the second-named speaker) suggesting that the ranks of elliptic curves in families of quadratic twists are bounded. The computing project itself was run by Mark Watkins, with assistance from Steve Donnelly, Noam Elkies, Nick Rogers and the first-named speaker.

This talk is part of the Number Theory Seminar series.

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