Let be an elliptic curve defined over , the finite field of elements. We show that for some constant depending only on , there are infinitely many positive integers such that the exponent of , the group of -rational points on , is at most . This is an analogue of a result of R. Schoof on the exponent of the group of -rational points, when a fixed elliptic curve is defined over and the prime tends to infinity.
Soit une courbe elliptique définie sur , le corps fini à éléments. Nous montrons que pour une constante dépendant seulement de , il existe une infinité d’entiers positifs tels que l’exposant de , le groupe des points -rationnels sur , est au plus . Il s’agit d’un analogue d’un résultat de R. Schoof sur l’exposant du groupe des points -rationnels, lorsqu’une courbe elliptique fixée est définie sur et le nombre premier tend vers l’infini.
@article{JTNB_2006__18_2_471_0, author = {Luca, Florian and McKee, James and Shparlinski, Igor E.}, title = {Small exponent point groups on elliptic curves}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {471--476}, publisher = {Universit\'e Bordeaux 1}, volume = {18}, number = {2}, year = {2006}, doi = {10.5802/jtnb.554}, zbl = {05135399}, mrnumber = {2289434}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.554/} }
TY - JOUR AU - Luca, Florian AU - McKee, James AU - Shparlinski, Igor E. TI - Small exponent point groups on elliptic curves JO - Journal de théorie des nombres de Bordeaux PY - 2006 SP - 471 EP - 476 VL - 18 IS - 2 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.554/ DO - 10.5802/jtnb.554 LA - en ID - JTNB_2006__18_2_471_0 ER -
%0 Journal Article %A Luca, Florian %A McKee, James %A Shparlinski, Igor E. %T Small exponent point groups on elliptic curves %J Journal de théorie des nombres de Bordeaux %D 2006 %P 471-476 %V 18 %N 2 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.554/ %R 10.5802/jtnb.554 %G en %F JTNB_2006__18_2_471_0
Luca, Florian; McKee, James; Shparlinski, Igor E. Small exponent point groups on elliptic curves. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 2, pp. 471-476. doi : 10.5802/jtnb.554. http://www.numdam.org/articles/10.5802/jtnb.554/
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