Courbes elliptiques sur $\Bbb Q$, ayant un point d'ordre $2$ rationnel sur $\Bbb Q$, de conducteur $2^Np$

Tom 429 / 2004

Wilfrid Ivorra Dissertationes Mathematicae 429 (2004), 1-55 MSC: Primary 11G05 DOI: 10.4064/dm429-0-1


\def\Q{{\sym Q}}Let $p$ be a prime number $\geq 29$ and $N$ be a positive integer. In this paper, we are interested in the problem of the determination, up to $\Q$-isomorphism, of all the elliptic curves over $\Q$ whose conductor is $2^Np$, with at least one rational point of order $2$ over $\Q$. This problem was studied in 1974 by B.~Setzer in case $N=0$. Consequently, in this work we are concerned with the case $N\geq 1$. The results presented here are analogous to those obtained by B. Setzer and allow one in practice to find a complete list of such curves.


  • Wilfrid IvorraUMR 7586 du CNRS, Équipe de Théorie des Nombres
    Institut de Mathématiques
    Université Paris VI
    175 Rue du Chevaleret
    Paris 75013, France

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