Rational and Elliptic Parametrizations ofQ-Curves
Rational and Elliptic Parametrizations ofQ-Curves
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DOI：
10.1006/jnth.1998.2259
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发表时间：
1998-09
影响因子：
0.7
通讯作者：
Josep González;J. Lario
中科院分区：
文献类型：
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作者：
Josep González;J. Lario
本文给出了代数曲线X *（N）的有理点的显式参数化，X *（N）是模曲线X 0（N）与Atkin-Lehner对合生成的群B（N）的商，当N是无平方数的有理曲线或椭圆曲线时。通过考虑X *（N）的模解释，沿着标准的“有界性”猜想，我们得到了除有限集之外的所有Q -曲线的Q -等距类.
Abstract We describe explicit parametrizations of the rational points of X *( N ), the algebraic curve obtained as quotient of the modular curve X 0 ( N ) by the group B ( N ) generated by the Atkin–Lehner involutions, whenever N is square-free and the curve is rational or elliptic. By taking into account the moduli interpretation of X *( N ), along with a standard “boundedness” conjecture, we obtain all the Q -isogeny classes of Q -curves except for a finite set.