A note on the rational points of X_0^+(N)
Number Theory
2007-05-23 v3 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0508115,
title = {A note on the rational points of X_0^+(N)},
author = {Carlos Castano-Bernard},
journal= {arXiv preprint arXiv:math/0508115},
year = {2007}
}
Comments
11 pages, 9 figures