2008 AMC 12B Problem 17

Let A, B and C be three distinct points on the graph of y=x^2 such that line AB is parallel to the x-axis and \triangle ABC is a right triangle with area 2008. What is the sum of the digits of the y-coordinate of C?

\textbf{(A)}\ 16\qquad\textbf{(B)}\ 17\qquad\textbf{(C)}\ 18\qquad\textbf{(D)}\ 19\qquad\textbf{(E)}\ 20

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.