On group structures realized by elliptic curves over a fixed finite field | Macquarie University ResearchOnline

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Title: On group structures realized by elliptic curves over a fixed finite field
Related: Experimental mathematics, Vol. 21, No. 1, (2012), p.1-10
DOI: 10.1080/10586458.2012.632754
Publisher: Taylor & Francis
Date: 2012
Author/Creator: Farashahi, Reza Rezaeian
Author/Creator: Shparlinski, Igor E
Description: We obtain explicit formulas for the number of nonisomorphic elliptic curves with a given group structure (considered as an abstract abelian group) and the number of distinct group structures of all elliptic curves over a finite field. We use these formulas to derive some asymptotic estimates and tight upper and lower bounds for various counting functions related to classification of elliptic curves according to their group structure. Finally, we present results of some numerical tests that exhibit several interesting phenomena in the distribution of group structures.
Description: 10 page(s)
Subject Keyword: elliptic curve
Subject Keyword: finite field
Subject Keyword: group structure
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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