English

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

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