REPRESENTATION OF PRIMES BY THE PRINCIPAL FORM OF NEGATIVE DISCRIMINANT $\Delta$ WHEN $h(\Delta)$ IS 4

Let $\Delta$ be a negative integer which is congruent to 0 or 1 (mod 4). Let $H(\Delta)$ denote the form class group of classes of positive-definite, primitive integral binary quadratic forms $ax^2 +bxy +cy^2$ of discriminant $\Delta$. If $H(\Delta)$ is a cyclic group of order 4, an explicit quartic polynomial $\rho \Delta(x)$ of the form $x^4-bx^2 +d$ with integral coefficients is determined such that for an odd prime $p$ not dividing $\Delta$, $p$ is represented by the principal form of discriminant $\Delta$ if and only if the congruence $\rho \Delta(x) \equiv 0$ (mod $p$) has four solutions.