Displaying similar documents to “Computing modular degrees using L -functions”

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...

Involutory elliptic curves over 𝔽 q ( T )

Andreas Schweizer (1998)

Journal de théorie des nombres de Bordeaux

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For n ∈ 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.

Arithmetic of elliptic curves and diophantine equations

Loïc Merel (1999)

Journal de théorie des nombres de Bordeaux

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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.

Critical and ramification points of the modular parametrization of an elliptic curve

Christophe Delaunay (2005)

Journal de Théorie des Nombres de Bordeaux

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Let E be an elliptic curve defined over ℚ with conductor N and denote by ϕ the modular parametrization: ϕ : X 0 ( N ) → E ( ℂ ) . In this paper, we are concerned with the critical and ramification points of ϕ . In particular, we explain how we can obtain a more or less experimental study of these points.

Arakelov computations in genus 3 curves

Jordi Guàrdia (2001)

Journal de théorie des nombres de Bordeaux

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Arakelov invariants of arithmetic surfaces are well known for genus 1 and 2 ([4], [2]). In this note, we study the modular height and the Arakelov self-intersection for a family of curves of genus 3 with many automorphisms: C n : Y 4 = X 4 - ( 4 n - 2 ) X 2 Z 2 + Z 4 . Arakelov calculus involves both analytic and arithmetic computations. We express the periods of the curve C n in terms of elliptic integrals. The substitutions used in these integrals provide a splitting of the jacobian of C n as a product of...