Abstract
We derive formulas for the probabilities of various properties (cyclicity, squarefreeness, generation by random points) of the point groups of randomly chosen elliptic curves over random prime fields.
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Gekeler, EU. Statistics about elliptic curves over finite prime fields. manuscripta math. 127, 55–67 (2008). https://doi.org/10.1007/s00229-008-0192-9
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DOI: https://doi.org/10.1007/s00229-008-0192-9