A generalized Fermat curve of type (k, 3), where k >= 2, is a closed Riemann surface admitting a group H congruent to Z(k)(3) as a group of conformal automorphisms so that the quotient orbifold S / H is the Riemann sphere and it has exactly 4 cone points, each one of order k. Every genus one Riemann surface is a generalized Fermat curve of type (2, 3) and, if k >= 3, then a generalized Fermat curve of type (k, 3) is non-hyperelliptic. For each generalized Fermat curve, we compute its field of moduli and note that it is a field of definition. Moreover, for k = e(2i pi/P), where p >= 5 is a prime integer, we produce explicit algebraic models over the corresponding field of moduli. As a byproduct, we observe that the absolute Galois group Gal((Q) over bar /Q) acts faithfully at the level of non-hyperelliptic dessins d'enfants. This last fact was already known for dessins of genus 0, 1 and for hyperelliptic ones, but it seems that the non-hyperelliptic situation is not explicitly given in the existent literature. (C) 2014 Elsevier Ltd. All rights reserved.Regular 2015FONDECYTFONDECYT