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Rational and elliptic parametrizations of Q-Curves

Autor
Gonzalez, J.; Lario, J.-C.
Tipus d'activitat
Article en revista
Revista
Journal of number theory
Data de publicació
1998-11
Volum
72
Número
1
Pàgina inicial
13
Pàgina final
31
DOI
https://doi.org/10.1006/jnth.1998.2259 Obrir en finestra nova
Repositori
http://wstein.org/people/goins/lario.pdf Obrir en finestra nova
URL
http://www.sciencedirect.com/science/article/pii/S0022314X98922594/pdf?md5=cf969291a5ac8ca100aa17d6b985bd43&pid=1-s2.0-S0022314X98922594-main.pdf Obrir en finestra nova
Resum
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.
Grup de recerca
TN - Grup de Recerca en Teoria de Nombres

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