On group structures realized by elliptic curves over a fixed finite field

Reza Rezaeian Farashahi, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalExperimental Mathematics
Volume21
Issue number1
DOIs
Publication statusPublished - 2012

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