Explicit moduli spaces for congruences of elliptic curves
classification
🧮 math.NT
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ellipticcurvesdetermineexplicitsurfacebirationalcasecases
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We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil lattice and the geometric Picard number.
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