$K_2$ of elliptic curves with sufficient torsion over $Q$

Raymond Ross

Displaying similar documents to “ $K_{2}$ of elliptic curves with sufficient torsion over $Q$ ”

Explicit $p$ -descent for elliptic curves in characteristic $p$

J. F. Voloch (1990)

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Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.

Carlos Munuera Gómez (1991)

Extracta Mathematicae

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Let p be a prime number, p ≠ 2,3 and F_p the finite field with p elements. An elliptic curve E over F_p is a projective nonsingular curve of genus 1 defined over F_p. Each one of these curves has an isomorphic model given by an (Weierstrass) equation E: y² = x³ + Ax + B, A,B ∈ F_p with D = 4A³ + 27B² ≠ 0. The j-invariant of E is defined...

From the elliptic regulator to exotic relations.

Touafek, Nouressadat (2008)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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On the group orders of elliptic curves over finite fields

Everett W. Howe (1993)

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Variation of the root number in families of elliptic curves

David E. Rohrlich (1993)

Compositio Mathematica

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On the Tate-Shafarevich group of semistable elliptic curves with a rational 3-torsion

Noboru Aoki (2004)

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Involutory elliptic curves over $𝔽_{q} (T)$

Andreas Schweizer (1998)

Journal de théorie des nombres de Bordeaux

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For $n \in 𝔽_{q} [T]$ let $G$ be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve $X_{0} (𝔫)$ . We determine all $𝔫$ and $G$ for which the quotient curve $G ∖ X_{0} (𝔫)$ is rational or elliptic.

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 number of elliptic curves with CM cover large algebraic fields

Gerhard Frey, Moshe Jarden (2005)

Annales de l'institut Fourier

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Elliptic curves with CM unveil a new phenomenon in the theory of large algebraic fields. Rather than drawing a line between $0$ and $1$ or $1$ and $2$ they give an example where the line goes beween $2$ and $3$ and another one where the line goes between $3$ and $4$ .

Counting elliptic curves of bounded Faltings height

Ruthi Hortsch (2016)

Acta Arithmetica

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We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².

Displaying similar documents to “ K 2 of elliptic curves with sufficient torsion over Q ”

Displaying similar documents to “ $K_{2}$ of elliptic curves with sufficient torsion over $Q$ ”