We give an algorithm to compute the modular degree of an elliptic curve defined over . Our method is based on the computation of the special value at of the symmetric square of the -function attached to the elliptic curve. This method is quite efficient and easy to implement.
Nous donnons un algorithme pour calculer le degré modulaire d’une courbe elliptique définie sur . Notre méthode est basée sur le calcul de la valeur spéciale en du carré symétrique de la fonction attachée à la courbe elliptique. Cette méthode est assez efficace et facile à implémenter.
@article{JTNB_2003__15_3_673_0, author = {Delaunay, Christophe}, title = {Computing modular degrees using $L$-functions}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {673--682}, publisher = {Universit\'e Bordeaux I}, volume = {15}, number = {3}, year = {2003}, mrnumber = {2142230}, zbl = {1070.11021}, language = {en}, url = {http://www.numdam.org/item/JTNB_2003__15_3_673_0/} }
Delaunay, Christophe. Computing modular degrees using $L$-functions. Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 3, pp. 673-682. http://www.numdam.org/item/JTNB_2003__15_3_673_0/
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