Abstract
Let E be an elliptic curve defined over a number field K and let S be a density-one set of primes of K of good reduction for E. Faltings proved in 1983 that the K-isogeny class of E is characterized by the function p bar right arrow #E(k(p)), which maps a prime p is an element of S to the order of the group of points of E over the corresponding field k(p). We show that, in this statement, the ...
Abstract
Let E be an elliptic curve defined over a number field K and let S be a density-one set of primes of K of good reduction for E. Faltings proved in 1983 that the K-isogeny class of E is characterized by the function p bar right arrow #E(k(p)), which maps a prime p is an element of S to the order of the group of points of E over the corresponding field k(p). We show that, in this statement, the integer #E(k(p)) can be replaced by its radical. (c) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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