If we have an elliptic curve over $\Bbb F_p$ of the form: $$ y^2 = x^3 + ax + b \ , $$ $a, b$ belonging to $\Bbb F_p$, the discriminant is defined as: $$ D = -16(4a^3 + 27b^2)\ . $$ My question is: the calculation of $D$ should be done in $\Bbb F_p$? That is, is $D$ in $\Bbb F_p$? If not, in which ring should calculations be done?
Thank you.