Open Access
Translator Disclaimer
2009 A Note on the Rational Points of $X_0^+(N)$
Carlos Castaño-Bernard
Experiment. Math. 18(2): 129-135 (2009).

Abstract

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.

Citation

Download Citation

Carlos Castaño-Bernard. "A Note on the Rational Points of $X_0^+(N)$." Experiment. Math. 18 (2) 129 - 135, 2009.

Information

Published: 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1186.14023
MathSciNet: MR2549684

Subjects:
Primary: 14G05
Secondary: 11G18 , 14G35

Keywords: Heegner points , hyperplanes , modular curve

Rights: Copyright © 2009 A K Peters, Ltd.

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.18 • No. 2 • 2009
Back to Top