most recent 30 from http://mathoverflow.net 2013-06-19T15:25:58Z http://mathoverflow.net/feeds/user/21245 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/87916/simple-proofs-for-the-existence-of-elliptic-curves-having-a-given-number-of-point/87944#87944 anonymous 2012-02-09T00:57:50Z 2012-02-09T00:57:50Z

<p>You can compute the average and standard deviation of the number of points on y^2=f, choosing f randomly. That should give you (something close to) what you wanted about H_p': there must be an elliptic curve with that number of points, otherwise standard deviation would be too small. (Also, you can always twist so you have more than p+1 points rather than less.) </p>