On the distribution of analytic  values on quadratic twists of elliptic curves.

Quattrini, Patricia L.

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Loïc Merel (1999)

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We give a survey of methods used to connect the study of ternary diophantine equations to modern techniques coming from the theory of modular forms.

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We examine a class of modular functions for $Γ^{0} (N)$ whose values generate ring class fields of imaginary quadratic orders. This fact leads to a new algorithm for constructing elliptic curves with complex multiplication. The difficulties arising when the genus of $X_{0} (N)$ is not zero are overcome by computing certain modular polynomials. Being a product of four $η$ -functions, the proposed modular functions can be viewed as a natural generalisation of the functions examined by Weber and usually...

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Displaying similar documents to “On the distribution of analytic | Sh | values on quadratic twists of elliptic curves.”

Displaying similar documents to “On the distribution of analytic $\sqrt{| Sh |}$ values on quadratic twists of elliptic curves.”