  The Shimura-Taniyama conjecture states that the Mellin transform of the
Hasse-Weil L-function of any elliptic curve defined over the rational numbers
is a modular form. Recent work of Wiles, Taylor-Wiles and
Breuil-Conrad-Diamond-Taylor has provided a proof of this longstanding
conjecture. Elliptic curves provide the simplest framework for a class of
Calabi-Yau manifolds which have been conjectured to be exactly solvable. It is
shown that the Hasse-Weil modular form determined by the arithmetic structure
of the Fermat type elliptic curve is related in a natural way to a modular form
arising from the character of a conformal field theory derived from an affine
Kac-Moody algebra.
