A note on the rational points of X_0^+(N)

Details A note on the rational points of X_0^+(N) A note on the rational points of X_0^+(N)

2005-08-06

arxiv.org/abs/math/0508115v3

Mathematics

Number Theory

11 pages, 9 figures

Scientific paper

Let C be the image of a canonical embedding C of the Atkin-Lehner quotient X+0(N) associated to the Fricke involution wN. In this note we exhibit some relations among the rational points of C. For each g = 3 (resp. the first g = 4) curve C we found that there are one or more lines (resp. planes) in projectie space 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 non-hyperelliptic exceptional rational point.

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