A Note on the Rational Points of $X_0^+(N)$
Castaño-Bernard, Carlos
Experiment. Math., Tome 18 (2009) no. 1, p. 129-135 / Harvested from Project Euclid
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Let $C$ be the image of a canonical embedding $\phi$ of the Atkin--Lehner quotient $X_0^+(N)$ associated with the Fricke involution $w_N$. In this note we exhibit some relations among the rational points of $C$. For each $g=3$ (respectively the first $g=4$) curve $C$ we found that there are one or more lines (respectively planes) in $\PP^{g-1}$ whose intersection with $C$ consists entirely of rational Heegner points or the cusp point, where $N$ is prime. We also discuss an explanation of the first nonhyperelliptic exceptional rational point.
Publié le : 2009-05-15
Classification:  Modular curve,  Heegner points,  hyperplanes,  14G05,  11G18,  14G35 
@article{1259158425,
     author = {Casta\~no-Bernard, Carlos},
     title = {A Note on the Rational Points of $X\_0^+(N)$},
     journal = {Experiment. Math.},
     volume = {18},
     number = {1},
     year = {2009},
     pages = { 129-135},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1259158425}
}

Castaño-Bernard, Carlos. A Note on the Rational Points of $X_0^+(N)$. Experiment. Math., Tome 18 (2009) no. 1, pp.  129-135. http://gdmltest.u-ga.fr/item/1259158425/