Abstract
The aim of this paper is to analyze the distribution of analytic (and signed) square roots of III values on imaginary quadratic twists of elliptic curves. Given an elliptic curve E of rank zero and prime conductor N, there is a weight- modular form g associated with it such that the d-coefficient of g is related to the value at s = 1 of the L-series of the (-d)-quadratic twist of the elliptic curve E. Assuming the Birch and Swinnerton-Dyer conjecture, we can then calculate for a large number of integers d the order of X of the (-d)-quadratic twist of E and analyze their distribution.
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