Abelian varieties up to isogeny

Okay, imagine you have a bunch of toy cars that look the same but they have different colors. Now imagine you have a way to change the way the cars move, like changing the wheels or adding an engine. These changes make the cars move differently but they still look the same on the outside.

In math, we have something called abelian varieties. They are like these toy cars, they look the same but they have different properties. And just like the toy cars, we can change the properties of abelian varieties without changing the way they look. This is called an isogeny.

So basically, abelian varieties up to isogeny means that we are looking at abelian varieties that look the same but have different properties, and we can change the properties without changing the way they look.