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SUMMARY:Ranks of quadratic twists of elliptic curves (Please note change i
 n time) - Tom Fisher (Cambridge) / Andrew Granville (UCL)
DTSTART:20151013T134500Z
DTEND:20151013T144500Z
UID:TALK61446@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:We report on a large-scale project searching for congruent\nnu
 mber elliptic curves of large rank. As a result of these\ninvestigations t
 here are now 27 curves known of rank 7\, but none of\nrank 8. The methods 
 used to exclude candidate curves include higher\ndescents\, and bounds on 
 the analytic rank. We   explain a heuristic\n(of the second-named speaker)
  suggesting that the ranks of elliptic\ncurves in  families of quadratic t
 wists are bounded. The computing\nproject itself was run by Mark Watkins\,
  with assistance from Steve\nDonnelly\, Noam Elkies\, Nick Rogers and the 
 first-named speaker.
LOCATION:MR13
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