On the L-functions of the curves y2 = xl + A

Let l > 3 be an odd prime and let A be an integer not divisible by l. Let C(A) be the non-singular projective model over of the affine curve C(A): y(2) = x(l) + A. In this paper, we use the theory of Hilbert modular Eisenstein series to obtain a formula for the central value of the Hasse-Weil L-function L(C(A), s) of the curve C(A) when the cyclotomic field (zeta(l)) has ideal class number 1.