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Rational and elliptic parametrizations of Q-Curves

Author
Gonzalez, J.; Lario, J.-C.
Type of activity
Journal article
Journal
Journal of number theory
Date of publication
1998-11
Volume
72
Number
1
First page
13
Last page
31
DOI
https://doi.org/10.1006/jnth.1998.2259 Open in new window
Repository
http://wstein.org/people/goins/lario.pdf Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0022314X98922594/pdf?md5=cf969291a5ac8ca100aa17d6b985bd43&pid=1-s2.0-S0022314X98922594-main.pdf Open in new window
Abstract
We describe explicit parametrizations of the rational points ofX*(N), the algebraic curve obtained as quotient of the modular curveX0(N) by the groupB(N) generated by the Atkin–Lehner involutions, wheneverNis square-free and the curve is rational or elliptic. By taking into account the moduli interpretation ofX*(N), along with a standard “boundedness” conjecture, we obtain all theQ-isogeny classes ofQ-curves except for a finite set.
Group of research
TN - Number Theory Research Group

Participants