I am trying to find an as simple as possible example of a Weierstrass equation where the eta quotient exists and is not completely trivial.
What would be the eta quotient for the Weierstrass equation $x^2 = y^2$ ?
At $n$ equal to a squarefree number it should be equal to https://oeis.org/A366562 or the conjectured form:
a(n) = [Mod[n, 2] = 1]A000010(n)*(-1)^A001221(n).