On the number of elliptic curves with CM cover large algebraic fields

Gerhard Frey; Moshe Jarden

Displaying similar documents to “On the number of elliptic curves with CM cover large algebraic fields”

$K_{2}$ of elliptic curves with sufficient torsion over $Q$

Raymond Ross (1992)

Compositio Mathematica

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Good reduction of elliptic curves over imaginary quadratic fields

Masanari Kida (2001)

Journal de théorie des nombres de Bordeaux

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We prove that the $j$ -invariant of an elliptic curve defined over an imaginary quadratic number field having good reduction everywhere satisfies certain Diophantine equations under some hypothesis on the arithmetic of the quadratic field. By solving the Diophantine equations explicitly in the rings of quadratic integers, we show the non-existence of such elliptic curve for certain imaginary quadratic fields. This extends the results due to Setzer and Stroeker.

Non-vanishing of $n$ -th derivatives of twisted elliptic $L$ -functions in the critical point

Jacek Pomykała (1997)

Journal de théorie des nombres de Bordeaux

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Let $E$ be a modular elliptic curve over $ℚ$ $L^{(n)} (s, E)$ denote the $n$ -th derivative of its Hasse-Weil $L$ -series. We estimate the number of twisted elliptic curves $E_{d}, d \leq D$ such that $L^{(n)} (1, E_{d}) \neq 0$ .

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...

On the group orders of elliptic curves over finite fields

Everett W. Howe (1993)

Compositio Mathematica

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Supersingular primes for elliptic curves over real number fields

Noam D. Elkies (1989)

Compositio Mathematica

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Primitive points on elliptic curves

Rajiv Gupta, M. Ram Murty (1986)

Compositio Mathematica

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$S$ -integral points on elliptic curves - Notes on a paper of B. M. M. de Weger

Emanuel Herrmann, Attila Pethö (2001)

Journal de théorie des nombres de Bordeaux

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In this paper we give a much shorter proof for a result of B.M.M de Weger. For this purpose we use the theory of linear forms in complex and $p$ -adic elliptic logarithms. To obtain an upper bound for these linear forms we compare the results of Hajdu and Herendi and Rémond and Urfels.

Counting points of small height on elliptic curves

D.W. Masser (1989)

Bulletin de la Société Mathématique de France

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