A Legendre-symbol formula for $D_p(3,1)$

Let $D_p(c,d)$ denote the determinant associated with the quadratic form $i^2+cij+dj^2$ in the paper. Legendre-symbol formula. For any odd prime $p\equiv\pm2\pmod5$,

$$\left(\frac{D_p(3,1)}{p}\right)= \begin{cases} \left(\frac{6}{p}\right)&\text{if }p\equiv1\pmod4,\\\\ 0&\text{if }p\equiv3\pmod4. \end{cases}$$

The supplied text gives no resolution of this proposed formula.