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In this paper we determine the quadratic points on the modular curves X 0 (N) X₀ (N), where the curve is non-hyperelliptic, the genus is 3 3, 4 4, or 5 5, and the Mordell–Weil group of J 0 (N) J₀ (N) is finite. The values of N N are 34 34, 38 38, 42 42, 44 44, 45 45, 51 51, 52 52, 54 54, 55 55, 56 56, 63 63, 64 64, 72 72, <i
Özman et al. (Wed,) studied this question.
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