Geodesic
Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 409-417

Voir la notice de l'article provenant de la source Cambridge University Press

We show that, for most of the elliptic curves $\text{E}$ over a prime finite field ${{\mathbb{F}}_{p}}$ of $p$ elements, the discriminant $D\left( E \right)$ of the quadratic number field containing the endomorphism ring of $\text{E}$ over ${{\mathbb{F}}_{p}}$ is sufficiently large. We also obtain an asymptotic formula for the number of distinct quadratic number fields generated by the endomorphism rings of all elliptic curves over ${{\mathbb{F}}_{p}}$ .
DOI : 10.4153/CMB-2007-039-2
Mots-clés : 11G20, 11N32, 11R11 
Luca, Florian; Shparlinski, Igor E. Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 409-417. doi: 10.4153/CMB-2007-039-2
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