Each mod form and each ellip curve have a series of numbers associated, some clever spark noticed those series appeared in pairs. One mod form would have the same series as a corresponding ellip curve, even though they were completely different types of object.
If you find a way to fully describe an object and two objects share that description, they are the same object.
If they don't look like the same object then the way in which you define the object needs to change.
Does something about modular forms tell you something otherwise unknown about elliptic curves?
Would this help in problem at the basis of encryption?
This raises some very interesting questions.
Exactly, extending mathematical problems into extra dimensions often trivialises them.
Including properties (descriptive) can often be analogous to adding dimensions. Abstractly, these things are equivalent.
E.g. including a time dimension to a spatial one can give velocity. To a displacement property can give acceleration, etc. Adding a nasal dimension can separate elephants out from other mammals, etc.