2 4 N ov 2 01 4 Functions and differentials on the non - split Cartan modular curve of level
نویسنده
چکیده
The genus 4 modular curve Xns(11) attached to a non-split Cartan group of level 11 admits a model defined over Q. We compute generators for its function field in terms of Siegel modular functions. We also show that its Jacobian is isomorphic over Q to the new part of the Jacobian of the classical modular curve X0(121).
منابع مشابه
Integral points of a modular curve of level 11
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 i...
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We prove that there exists an integer p0 such that X split (p)(Q) is made of cusps and CM-points for any prime p > p0. Equivalently, for any non-CM elliptic curve E over Q and any prime p > p0 the image of Gal(¯ Q/Q) by the representation induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an ol...
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