2020 AMC 10B Problem 9

How many ordered pairs of integers $(x,y)$ satisfy the equation $x^{2020} + y^2 = 2y?$

$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ \text{infinitely many}$

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