2016 AMC 12B Problem 6

All three vertices of \bigtriangleup ABC lie on the parabola defined by y=x^2, with A at the origin and \overline{BC} parallel to the x-axis. The area of the triangle is 64. What is the length of BC?

\textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 16

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