Article published in the proceeding of the conference CAI 2015 http://www.ims.uni-stuttgart.de/events/CAI2015 ; In this paper, we generalize the method of Scott and Barreto in order to construct a family of pairing-friendly elliptic curve. We present an explicit algorithm to obtain generalized MNT families curves with any cofactors. We also analyze the complex multiplication equations of these curves and transform them into generalized Pell equation. As an example, we describe a way to generate Edwards curves with embedding degree 6.