Number Theory
On the prime divisors of the number of points on an elliptic curve
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 1-3.

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#E(kp), which maps a prime pS to the order of the group of points of E over the corresponding field kp. We show that, in this statement, the integer #E(kp) can be replaced by its radical.

Soit E une courbe elliptique définie sur un corps de nombres K, et soit S un ensemble de densité 1 de places de K en lesquelles E a bonne réduction. Faltings a montré en 1983 que la classe de K-isogénie de E est caracterisée par la fonction p#E(kp), qui envoie chaque place pS sur lʼordre du groupe des points de E sur le corps résiduel correspondant. On montre quʼil suffit de considérer les nombres premiers divisant cet ordre.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.01.003
Hall, Chris 1; Perucca, Antonella 2

1 University of Wyoming, United States
2 University of Regensburg, Germany
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Hall, Chris; Perucca, Antonella. On the prime divisors of the number of points on an elliptic curve. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 1-3. doi : 10.1016/j.crma.2013.01.003. http://www.numdam.org/articles/10.1016/j.crma.2013.01.003/

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