Reductions of points on elliptic curves |
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| Authors: | Amir Akbary Dragos Ghioca V. Kumar Murty |
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| Affiliation: | 1. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada
2. Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
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| Abstract: | ![]()
Let E be an elliptic curve defined over mathbbQ{mathbb{Q}}. Let Γ be a subgroup of rank r of the group of rational points E(mathbbQ){E(mathbb{Q})} of E. For any prime p of good reduction, let [`(G)]{bar{Gamma}} be the reduction of Γ modulo p. Under certain standard assumptions, we prove that for almost all primes p (i.e. for a set of primes of density one), we have | |[`(G)]| 3 fracpf(p),|bar{Gamma}| geq frac{p}{f(p)}, |
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