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

Christophe Delaunay[1]

  • [1] Institut Camille Jordan Bâtiment Braconnier Université Claude Bernard Lyon 1 43, avenue du 11 novembre 1918 69622 Villeurbanne cedex, France

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 109-124
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Delaunay, Christophe. "Critical and ramification points of the modular parametrization of an elliptic curve." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 109-124. <http://eudml.org/doc/249431>.

@article{Delaunay2005,
abstract = {Let $E$ be an elliptic curve defined over $\mathbb\{Q\}$ with conductor $N$ and denote by $\varphi $ the modular parametrization:\[\varphi \; : \; X\_0(N) \rightarrow E(\mathbb\{C\}) \; .\]In this paper, we are concerned with the critical and ramification points of $\varphi $. In particular, we explain how we can obtain a more or less experimental study of these points.},
affiliation = {Institut Camille Jordan Bâtiment Braconnier Université Claude Bernard Lyon 1 43, avenue du 11 novembre 1918 69622 Villeurbanne cedex, France},
author = {Delaunay, Christophe},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {modular elliptic curves; critical points; ramification points; analytic rank; Hecke operator; involutory curve},
language = {eng},
number = {1},
pages = {109-124},
publisher = {Université Bordeaux 1},
title = {Critical and ramification points of the modular parametrization of an elliptic curve},
url = {http://eudml.org/doc/249431},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Delaunay, Christophe
TI - Critical and ramification points of the modular parametrization of an elliptic curve
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 109
EP - 124
AB - Let $E$ be an elliptic curve defined over $\mathbb{Q}$ with conductor $N$ and denote by $\varphi $ the modular parametrization:\[\varphi \; : \; X_0(N) \rightarrow E(\mathbb{C}) \; .\]In this paper, we are concerned with the critical and ramification points of $\varphi $. In particular, we explain how we can obtain a more or less experimental study of these points.
LA - eng
KW - modular elliptic curves; critical points; ramification points; analytic rank; Hecke operator; involutory curve
UR - http://eudml.org/doc/249431
ER -

References

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