There are several formulations of the conjecture. Showing that they are equivalent was a main challenge of number theory in the second half of the 20th century. The modularity of an elliptic curve of conductor can be expressed also by saying that there is a non-constant rational map defined over , from the modular curve to . In particular, the points of can be parametrized by modular functions.
There are several formulations of the conjecture. Showing that they are equivalent was a main challenge of number theory in the second half of the 20th century. The modularity of an elliptic curve o.f conductor can be expressed also by saying that there is a non-constant rational map defined over , from the modular curve to  In particular, the points of can be parametrized by modular functions.