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

R. R.  Farashahi,  I. E. Shparlinski, “On group structures realized by elliptic curves over a fixed finite field”, Experimental Mathematics, vol. 21, No 1, pp. 1-10, 2012. http://www.tandfonline.com/doi/abs/10.1080/10586458.2012.632754