Elliptic curves & Modular forms

Fermat's last theorem was proved by proving the Taniyama Shimura conjecture, i.e. the elliptic curves and modular forms are equal.

When the transformation of matrix takes place, the vectors are invariant, only the component changes. The eigenvectors of a square matrix after being multiplied remains parallel to the original vector.

The E-series of the elliptic curves, E2=4, E3=4 are the no.of possibilities, i.e. the total no.of whole no as per 'x','y'. E5 denotes clock arithmetic 5 with total possibility of 4.

The ingredients of a modular form are from M1,M2 to infinity.

M2=3, M3=2 where 3,2 are eigenvectors.

MY QUESTION IS HOW THEY ARE LINKED?

Is it that while transforming matrix, as the eigenvectors are invariant and E series follows the clock-arithmetic, in any way they are linked?

Kindly let me know.

Waiting eagerly for your reply.

-- Shounak