Abstract Let N ≥ 1 be an square free integer and let W N be a non-trivial subgroup of the group of the Atkin-Lehner involutions of X 0 ( N ) such that the modular curve X 0 ( N ) / W N has genus at least two. We determine all pairs ( N , W N ) such that X 0 ( N ) / W N is a bielliptic curve and the pairs ( N , W N ) such that X 0 ( N ) / W N has an infinite number of quadratic points over Q .

中文翻译：

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无 N 平方的双椭圆商模曲线

摘要 令 N ≥ 1 为自由平方整数，令 WN 为 X 0 ( N ) 的 Atkin-Lehner 对合群的非平凡子群，使得模曲线 X 0 ( N ) / WN 至少有属二。我们确定所有对 (N, WN) 使得 X 0 (N)/WN 是一条双椭圆曲线，并且确定所有对 (N, WN) 使得 X 0 (N)/WN 在 Q 上具有无限数量的二次点。