I have the following problems on my modular forms course final exam:
Over field $\mathbb{C}(\lambda)$ equation $y^2 =x(x−1)(x−\lambda)$ defines an elliptic curve $E_{\lambda}$ with a base in 2-torsion. Express $\lambda$ as a function of $z$ (curve $E_{\lambda}$ equals $\mathbb{C}/(\mathbb{Z+Z}z)$ ).
Unfortunately, I have no idea how one can solve it. So, any hints, links, solutions are more than welcome.