Rational points on $X_0^+ (N)$ and quadratic $\mathbb {Q}$-curves

Galbraith, Steven D.

Rational points on

X_{0}^{+} (N)

and quadratic

ℚ

-curves

Galbraith, Steven D.

Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 205-219.

Résumé
Abstract

Nous considérons les points rationnels sur $X_{0} (N) / W_{N}$ dans le cas où $N$ est un nombre composé. Nous faisons une étude de certains cas qui ne se déduisent pas des résultats de Momose. Des points rationnels sont obtenus pour $N = 91$ et $N = 125$ . Nous exhibons aussi les $j$ -invariants des $ℚ$ -courbes quadratiques correspondantes.

The rational points on $X_{0} (N) / W_{N}$ in the case where $N$ is a composite number are considered. A computational study of some of the cases not covered by the results of Momose is given. Exceptional rational points are found in the cases $N = 91$ and $N = 125$ and the $j$ -invariants of the corresponding quadratic $ℚ$ -curves are exhibited.

MR Zbl | 2 citations dans Numdam

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     title = {Rational points on $X_0^+ (N)$ and quadratic $\mathbb {Q}$-curves},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
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     publisher = {Universit\'e Bordeaux I},
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Galbraith, Steven D. Rational points on $X_0^+ (N)$ and quadratic $\mathbb {Q}$-curves. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 1, pp. 205-219. http://archive.numdam.org/item/JTNB_2002__14_1_205_0/

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