Good reduction of elliptic curves over imaginary quadratic fields

Masanari Kida

Displaying similar documents to “Good reduction of elliptic curves over imaginary quadratic fields”

Determination of elliptic curves with everywhere good reduction over real quadratic fields ℚ(√(3p))

Takaaki Kagawa (2001)

Acta Arithmetica

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On the number of large integer points on elliptic curves

P. G. Walsh (2009)

Acta Arithmetica

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Constructing elliptic curves over finite fields using double eta-quotients

Andreas Enge, Reinhard Schertz (2004)

Journal de Théorie des Nombres de Bordeaux

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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...

Counting points on elliptic curves over finite fields

René Schoof (1995)

Journal de théorie des nombres de Bordeaux

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We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic...