Assuming GRH, we present an algorithm which inputs a prime and outputs the set of fundamental discriminants such that the reduction map modulo a prime above from elliptic curves with CM by to supersingular elliptic curves in characteristic is surjective. In the algorithm we first determine an explicit constant so that implies that the map is necessarily surjective and then we compute explicitly the cases .
Sous GRH, nous présentons un algorithme qui, étant donné un nombre premier p, calcule l’ensemble des discriminants fondamentaux , tels que l’application de réduction, modulo un premier aux dessus de , des courbes elliptiques avec multiplication complexe par vers les courbes elliptiques supersingulières en caractéristique est surjective. Dans l’algorithme, nous déterminons d’abord une borne explicite telle que implique que l’application est nécessairement surjective et nous calculons ensuite explicitement les cas .
Keywords: Quaternion Algebra, Elliptic Curves, Maximal Orders, Half Integer Weight Modular Forms, Kohnen’s Plus Space, Shimura Lifts
@article{JTNB_2009__21_3_635_0, author = {Kane, Ben}, title = {CM liftings of supersingular elliptic curves}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {635--663}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {3}, year = {2009}, doi = {10.5802/jtnb.692}, zbl = {1214.11142}, mrnumber = {2605537}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.692/} }
TY - JOUR AU - Kane, Ben TI - CM liftings of supersingular elliptic curves JO - Journal de théorie des nombres de Bordeaux PY - 2009 SP - 635 EP - 663 VL - 21 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.692/ DO - 10.5802/jtnb.692 LA - en ID - JTNB_2009__21_3_635_0 ER -
Kane, Ben. CM liftings of supersingular elliptic curves. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 635-663. doi : 10.5802/jtnb.692. http://archive.numdam.org/articles/10.5802/jtnb.692/
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