The distribution of group structures on elliptic curves over finite prime fields
Ernst-Ulrich Gekeler
FR 6.1 Mathematik Universität des Saarlandes D-66041 Saarbrücken Germany
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Abstract
We determine the probability that a randomly chosen elliptic curve over a randomly chosen prime field has an -primary part isomorphic with a fixed abelian -group .
Probabilities for “ divisible by ”, “ cyclic and expectations for the number of elements of precise order in are derived, both for unbiased and for with .
Cite this article
Ernst-Ulrich Gekeler, The distribution of group structures on elliptic curves over finite prime fields. Doc. Math. 11 (2006), pp. 119–142
DOI 10.4171/DM/206