Abstract

of points of degree d of C. For quadratic points, that is, d=2, Abramovich and Harris show that the existence of infinitely many such points is equivalent to the fact that the curve C is either hyperelliptic or bielliptic, i.e., C has a degree two map to a projective line or an elliptic curve, respectively. In this work we shall study the family of modular curves X0(N) admitting infinitely many quadratic points. It consists of all the hyperelliptic and bielliptic curves. The family of hyperelliptic modular curves is completely determined by Ogg's contribution [10]. We shall settle here the bielliptic case. Our main result is:

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