First, stop this nonsense and learn algebraic geometry. After you're done with that, try reading Mumford's paper "Picard Groups of Moduli Problems", which is a fascinating window into the mind of one of the people who later invented algebraic stacks as he was himself figuring out what you are also trying to figure out. From that, you should have a sketch of how the properties of elliptic curves contribute to the properties of their moduli stack; make sure you work out or look up the various things he says about them. Then you can read a regular treatise on stacks.

You should really learn algebraic geometry first. After you're done with that, try reading Mumford's paper "Picard Groups of Moduli Problems", which is a fascinating window into the mind of one of the people who later invented algebraic stacks as he was himself figuring out what you are also trying to figure out. From that, you should have a sketch of how the properties of elliptic curves contribute to the properties of their moduli stack; make sure you work out or look up the various things he says about them. Then you can read a regular treatise on stacks.