The truth about torsion in the CM case

Clark, Pete L.; Pollack, Paul

Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 683-688.

Soit $T_{\mathit{CM}}(d)$ la taille maximale du sous-groupe de torsion d'une courbe elliptique à multiplications complexes, définie sur un corps de nombres de degré d. Nous montrons qu'il existe C une constante absolue, effective, telle que $T_{\mathit{CM}}(d)\le Cd\log \log (d)$ pour tout $d\ge 3$.

Let $T_{\mathbf{CM}}(d)$ be the maximum size of the torsion subgroup of an elliptic curve with complex multiplication over a degree d number field. We show there is an absolute, effective constant C such that $T_{\mathbf{CM}}(d)\le Cd\log \log d$ for all $d\ge 3$.

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