Computing modular degrees using L -functions

Christophe Delaunay

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 3, page 673-682
  • ISSN: 1246-7405

Abstract

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We give an algorithm to compute the modular degree of an elliptic curve defined over ℚ . Our method is based on the computation of the special value at s = 2 of the symmetric square of the L -function attached to the elliptic curve. This method is quite efficient and easy to implement.

How to cite

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Delaunay, Christophe. "Computing modular degrees using $L$-functions." Journal de théorie des nombres de Bordeaux 15.3 (2003): 673-682. <http://eudml.org/doc/249080>.

@article{Delaunay2003,
abstract = {We give an algorithm to compute the modular degree of an elliptic curve defined over $\mathbb \{Q\}$. Our method is based on the computation of the special value at $s = 2$ of the symmetric square of the $L$-function attached to the elliptic curve. This method is quite efficient and easy to implement.},
author = {Delaunay, Christophe},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {modular parametrization; elliptic curve; symmetric square},
language = {eng},
number = {3},
pages = {673-682},
publisher = {Université Bordeaux I},
title = {Computing modular degrees using $L$-functions},
url = {http://eudml.org/doc/249080},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Delaunay, Christophe
TI - Computing modular degrees using $L$-functions
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 3
SP - 673
EP - 682
AB - We give an algorithm to compute the modular degree of an elliptic curve defined over $\mathbb {Q}$. Our method is based on the computation of the special value at $s = 2$ of the symmetric square of the $L$-function attached to the elliptic curve. This method is quite efficient and easy to implement.
LA - eng
KW - modular parametrization; elliptic curve; symmetric square
UR - http://eudml.org/doc/249080
ER -

References

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  12. [12] E. Tollis, Zeros of Dedekind zeta functions in the critical strip. Math. Comp.66 (1997), 1295-1321. Zbl0877.11061MR1423079
  13. [13] M. Watkins, Computing the modular degree of an elliptic curve. Experimental Maths11 no. 4 (2003), 487-502. Zbl1162.11349MR1969641
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