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

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

2010-03-15

arxiv.org/abs/1003.3000v1

Mathematics

Number Theory

Scientific paper

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for 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 accordingly to their group structure. Finally, we present results of some numerical tests which exhibit several interesting phenomena in the distribution of group structures. We pose getting an explanation to these as an open problem.

Affiliated with

Also associated with

No associations

Rating

On group structures realized by elliptic curves over a fixed finite field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On group structures realized by elliptic curves over a fixed finite field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On group structures realized by elliptic curves over a fixed finite field will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215101