Elliptic curve notation

Question

This might be kind of a silly question about notation. I know:

$E$: an elliptic curve

$\mathbb{F_q}$: finite field

But I recently ran across the notation $E/\mathbb{F_q}$ for the first time, so does this mean an elliptic curve defined over a finite field?

Answer 1

In general, if $F$ is a field, and $V$ is a variety defined by polynomials defined over $F$, it is very common notation to write $V/F$ to indicate that "$V$ is defined over $F$", and simply read $V/F$ as "$V$ over $F$" or "$V$ defined over $F$" (so you interpret / as "over", and not as any type of quotient space).