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In algebraic geometry, a projective variety over an algebraically closed field $k$ is a subset of some projective $n$-space $\mathbb P^n$ over $k$ that is the zero-locus of some finite family of homogeneous polynomials of $n + 1$ variables with coefficients in $k$, that generate a prime ideal, the defining ideal of the variety

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How many elliptic curves over a finite field have a square discriminant?

$\newcommand{\char}{\operatorname{char}}$Given a finite field $F_q$ with $q\equiv 1 \bmod 3$ and $\char(F_q)>3$, I need to figure out how many isomorphism classes of elliptic curves $E/F_q$ have a squ …
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