 
Summary: July 7, 2009 15:24 WSPC/INSTRUCTION FILE vissqijnt
Squareness in the special Lvalue and special Lvalues of twists
Amod Agashe
Department of Mathematics, Florida State University
Tallahassee, FL 32306, U.S.A.
agashe@math.fsu.edu
Received (Day Month Year)
Accepted (Day Month Year)
Communicated by xxx
Let N be a prime and let A be a quotient of J0(N) over Q associated to a newform
such that the special Lvalue of A (at s = 1) is nonzero. Suppose that the algebraic
part of the special Lvalue of A is divisible by an odd prime q such that q does not
divide the numerator of N1
12
. Then the Birch and SwinnertonDyer conjecture predicts
that the qadic valuations of the algebraic part of the special Lvalue of A and of the
order of the ShafarevichTate group are both positive even numbers. Under a certain
mod q nonvanishing hypothesis on special Lvalues of twists of A, we show that the
qadic valuations of the algebraic part of the special Lvalue of A and of the Birch and
SwinnertonDyer conjectural order of the ShafarevichTate group of A are both positive
