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On the modular curves |
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| Authors: | Emmanuel Halberstadt Alain Kraus |
| Institution: | Université Paris VI, Laboratoire de Mathématiques Fondamentales, UFR 921, 4, place Jussieu, 75252 Paris Cedex 05, France ; Université Paris VI, Institut de Mathématiques, Case 247, 4, place Jussieu, 75252 Paris Cedex 05, France |
| Abstract: | Let  denote an elliptic curve over  and  the modular curve classifying the elliptic curves  over  such that the representations of  in the 7-torsion points of  and of  are symplectically isomorphic. In case  is given by a Weierstraß equation such that the  invariant is a square, we exhibit here nontrivial points of  . From this we deduce an infinite family of curves  for which  has at least four nontrivial points. |
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