We prove that the only rational point of the curve are the cusps.
Consequently, there does not exist any elliptic curve defined over which possesses a rational cyclic subgroup of order .
On démontre que les seuls points rationnels sur de la courbe sont les pointes.
En conséquence, il n’existe pas de courbe elliptique définie sur possédant un sous-groupe cyclique rationnel d’ordre .
@article{AIF_1980__30_2_17_0, author = {Mestre, Jean-Fran\c{c}ois}, title = {Points rationnels de la courbe modulaire $X_0(169)$}, journal = {Annales de l'Institut Fourier}, pages = {17--27}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {30}, number = {2}, year = {1980}, doi = {10.5802/aif.782}, mrnumber = {81h:10036}, zbl = {0432.14017}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.782/} }
TY - JOUR AU - Mestre, Jean-François TI - Points rationnels de la courbe modulaire $X_0(169)$ JO - Annales de l'Institut Fourier PY - 1980 SP - 17 EP - 27 VL - 30 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.782/ DO - 10.5802/aif.782 LA - fr ID - AIF_1980__30_2_17_0 ER -
Mestre, Jean-François. Points rationnels de la courbe modulaire $X_0(169)$. Annales de l'Institut Fourier, Volume 30 (1980) no. 2, pp. 17-27. doi : 10.5802/aif.782. http://www.numdam.org/articles/10.5802/aif.782/
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