The Denominator of the Special Value L(A<sub>f</sub>,1)/Omega(A<sub>f</sub>)

The Denominator of the Special Value L(A_{f},1)/Omega(A_{f})

Amod Agashe and William Stein

Let $f$ be a newform and $A_f$ the quotient
of $J_0(N)$ constructed by Shimura.
We prove that, up to a Manin constant and a power of $2$,
the denominator of the rational number $L(A_f,1)/\Omega(A_f)$
divides the order of the image of $(0)-(\infty)$ in .
This provides evidence for the Birch and Swinnerton-Dyer
conjecture and raises questions about the structure of .