How many primes $p$ are there such that $2p^4-7p^2+1$ is equal to square of an integer?

$ 
\textbf{(A)}\ 0
\qquad\textbf{(B)}\ 1
\qquad\textbf{(C)}\ 4
\qquad\textbf{(D)}\ \text{Infinitely many}
\qquad\textbf{(E)}\ \text{None of the preceding}
$