Rational points on X 0 + ( N ) and quadratic ℚ -curves

Steven D. Galbraith

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 1, page 205-219
  • ISSN: 1246-7405

Abstract

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The rational points on X 0 ( N ) / W N in the case where N is a composite number are considered. A computational study of some of the cases not covered by the results of Momose is given. Exceptional rational points are found in the cases N = 91 and N = 125 and the j -invariants of the corresponding quadratic ℚ -curves are exhibited.

How to cite

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Galbraith, Steven D.. "Rational points on $X_0^+ (N)$ and quadratic $\mathbb {Q}$-curves." Journal de théorie des nombres de Bordeaux 14.1 (2002): 205-219. <http://eudml.org/doc/248907>.

@article{Galbraith2002,
abstract = {The rational points on $X_0(N)/W_N$ in the case where $N$ is a composite number are considered. A computational study of some of the cases not covered by the results of Momose is given. Exceptional rational points are found in the cases $N = 91$ and $N = 125$ and the $j$-invariants of the corresponding quadratic $\mathbb \{Q\}$-curves are exhibited.},
author = {Galbraith, Steven D.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Heegner point; quadratic -curves; -invariants; modular curve; elliptic curves; exceptional rational points},
language = {eng},
number = {1},
pages = {205-219},
publisher = {Université Bordeaux I},
title = {Rational points on $X_0^+ (N)$ and quadratic $\mathbb \{Q\}$-curves},
url = {http://eudml.org/doc/248907},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Galbraith, Steven D.
TI - Rational points on $X_0^+ (N)$ and quadratic $\mathbb {Q}$-curves
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 1
SP - 205
EP - 219
AB - The rational points on $X_0(N)/W_N$ in the case where $N$ is a composite number are considered. A computational study of some of the cases not covered by the results of Momose is given. Exceptional rational points are found in the cases $N = 91$ and $N = 125$ and the $j$-invariants of the corresponding quadratic $\mathbb {Q}$-curves are exhibited.
LA - eng
KW - Heegner point; quadratic -curves; -invariants; modular curve; elliptic curves; exceptional rational points
UR - http://eudml.org/doc/248907
ER -

References

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