A Note on the Rational Points of X+0(N)
نویسنده
چکیده
Let C be the image of a canonical embedding φ 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 P 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.
منابع مشابه
A Note on the Rational Points
Let C be the image of a canonical embedding φ of the Atkin-Lehner quotient X + 0 (N) associated to the Fricke involution w N. Suppose φ is defined over the rationals. In this note we give some collinearity relations among rational points of C, for each X + 0 (N) of genus 3 and the first X + 0 (N) of genus 4, for N prime.
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ورودعنوان ژورنال:
- Experimental Mathematics
دوره 18 شماره
صفحات -
تاریخ انتشار 2009