Moduli stack of elliptic curves

Okay, kiddo, let me explain what a moduli stack of elliptic curves is. It's like a big toy box full of different kinds of toy cars, each with their own special features and designs.

Now, imagine that instead of toy cars, we have a bunch of elliptic curves. These are fancy math shapes that mathematicians like to play with. Just like how toy cars have different colors, shapes, and sizes, elliptic curves also have different properties, like how many points they have, how they're twisted, and how they're related to other curves.

The moduli stack of elliptic curves is like a way for mathematicians to organize and categorize all the different kinds of elliptic curves. It's like a big toy box with shelves and compartments for the different kinds of toy cars.

But it's not just about organization—it's also about understanding how different curves relate to each other. Just like how some toy cars can be grouped together based on their similarities, mathematicians can group elliptic curves together based on certain properties they share. They can look at how curves transform and change when you apply certain mathematical operations to them, and use that information to learn more about the curves themselves.

So, the moduli stack of elliptic curves is like a giant playground for mathematicians to explore and learn about these interesting and complex shapes. And just like with toy cars, the more you play with them, the more you discover about their unique features and qualities.