A quantitative primitive divisor result for points on elliptic curves
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, p. 609-634

Let E/K be an elliptic curve defined over a number field, and let PE(K) be a point of infinite order. It is natural to ask how many integers n1 fail to occur as the order of P modulo a prime of K. For K=, E a quadratic twist of y 2 =x 3 -x, and PE() as above, we show that there is at most one such n3.

Soient E/K une courbe elliptique définie sur un corps de nombres et PE(K) un point d’ordre infini. Il est naturel de se demander combien de nombres entiers n1 n’apparaissent pas comme ordre du point P modulo un idéal premier de K. Dans le cas où K=, E une tordue quadratique de y 2 =x 3 -x et PE() comme ci-dessus, nous démontrons qu’il existe au plus un tel n3.

DOI : https://doi.org/10.5802/jtnb.691
Classification:  11G05,  11B39
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     author = {Ingram, Patrick},
     title = {A quantitative primitive divisor result for points on elliptic curves},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {3},
     year = {2009},
     pages = {609-634},
     doi = {10.5802/jtnb.691},
     mrnumber = {2605536},
     zbl = {1208.11073},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2009__21_3_609_0}
}
Ingram, Patrick. A quantitative primitive divisor result for points on elliptic curves. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 609-634. doi : 10.5802/jtnb.691. http://www.numdam.org/item/JTNB_2009__21_3_609_0/

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