# Moduli space for elliptic curves

I would like to find a proof of the theorem which states that the family of elliptic curves over $\mathbb{C}$ is $1_{\mathbb{C}}$ dimensional. I'd be particularily happy to see the computation which reduces an arbitrary non-degenerate projective algebraic curve of third degree to Legendre's form $y^2z=x(x-z)(x-\lambda z)$, where $\lambda$ is the elliptic modulus. I have a book in which this is done, but the machinery used overwhelms me and I'd like to find another reference...