@article{10902/11302,
year = {2016},
url = {http://hdl.handle.net/10902/11302},
abstract = {Elliptic curves over a finite field Fq with j-invariant 0 or 1728, both supersingular and ordinary, whose embedding degree k is low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree with respect to a subgroup of prime order . For k = 1, 2, these conditions give parameterizations of q in terms of and two integers m, n. We show several examples of families with infinitely many curves. Similar parameterizations for k ? 3 need a fixed kth root of the unity in the underlying field. Moreover, when the elliptic curve admits distortion maps, an example is provided.},
publisher = {Taylor & Francis},
publisher = {International Journal of Computer Mathematics, 2016, Vol. 93, No. 12, 2042?2053},
title = {Elliptic curves with j = 0, 1728 and low embedding degree},
author = {Miret, Josep M. and Sadornil Renedo, Daniel and Tena, Juan G.},
}