Let p be a prime number ≥ 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 , 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 ≥ 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.
@book{bwmeta1.element.bwnjournal-article-doi-10_4064-dm429-0-1,
author = {Wilfrid Ivorra},
title = {Courbes elliptiques sur $\mathbb{Q}$, ayant un point d'ordre 2 rationnel sur $\mathbb{Q}$, de conducteur $2^{N}p$
},
series = {GDML\_Books},
year = {2004},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-dm429-0-1}
}
Wilfrid Ivorra. Courbes elliptiques sur ℚ, ayant un point d’ordre 2 rationnel sur ℚ, de conducteur $2^{N}p$
. GDML_Books (2004), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-dm429-0-1/