TY - JOUR
T1 - On group structures realized by elliptic curves over arbitrary finite fields
AU - Banks, William D.
AU - Pappalardi, Francesco
AU - Shparlinski, Igor E.
PY - 2012
Y1 - 2012
N2 - We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection that correspond to curves over prime fields or to curves with a prescribed torsion. Some of our results are rigorous and are based on recent advances in analytic number theory; some are conditional under certain widely believed conjectures; and others are purely heuristic in nature.
AB - We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection that correspond to curves over prime fields or to curves with a prescribed torsion. Some of our results are rigorous and are based on recent advances in analytic number theory; some are conditional under certain widely believed conjectures; and others are purely heuristic in nature.
UR - http://www.scopus.com/inward/record.url?scp=84874313948&partnerID=8YFLogxK
U2 - 10.1080/10586458.2011.606075
DO - 10.1080/10586458.2011.606075
M3 - Article
AN - SCOPUS:84874313948
SN - 1058-6458
VL - 21
SP - 11
EP - 25
JO - Experimental Mathematics
JF - Experimental Mathematics
IS - 1
ER -