On the number of elliptic curves with CM cover large algebraic fields
[Sur le nombre de courbes elliptiques avec CM sur des grands corps algèbriques]
Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2361-2374.

Les courbes elliptiques avec CM révèlent un nouveau phénomène dans la théorie des grands corps algébriques. Plutôt que de tracer une ligne entre 0 et 1 ou entre 1 et 2, elles fournissent un exemple où la ligne va de 2 à 3, ainsi qu’un exemple de ligne allant de 3 à 4

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.

DOI : 10.5802/aif.2163
Classification : 12E30
Keywords: Elliptic curves with CM, large algebraic fields, absolute Galois group, Haar measure, class number, Elliptic curves with CM, large algebraic fields, absolute Galois group, Haar measure, class number
Mot clés : courbes elliptiques avec CM, grands corps algébriques, groupe de Galois absolu, mesure de Haar, nombre de classes
Frey, Gerhard 1 ; Jarden, Moshe 2

1 Essen University, Institute for Experimental Mathematics, Ellernstrasse 29, 45326 Essen (Allemagne)
2 Tel Aviv University, School of Mathematics, Ramat Aviv, Tel Aviv 69978 (Israël)
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Frey, Gerhard; Jarden, Moshe. On the number of elliptic curves with CM cover large algebraic fields. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2361-2374. doi : 10.5802/aif.2163. http://www.numdam.org/articles/10.5802/aif.2163/

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