Integral points of a modular curve of level 11
نویسندگان
چکیده
Let Xns(11) denote the modular curve associated to the normalizer of a non-split Cartan subgroup of level 11; see [10, Appendix]. This curve has genus 1, is defined over Q and parametrizes elliptic curves with a certain level 11 structure. The interest of Theorem 1.1 lies in the fact that Xns(11) is isomorphic over Q to the curve E and that rational points (x, y) on E for which x/(xy − 11) is integral correspond precisely to integral points on Xns(11), i.e., to rational points for which the parametrized elliptic curve has its j-invariant in Z. We prove this in Section 4 and hence obtain the following corollary of Theorem 1.1.
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