Points rationnels de la courbe modulaire X 0 (169)
Mestre, Jean-François
Annales de l'Institut Fourier, Tome 30 (1980), p. 17-27 / Harvested from Numdam
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On démontre que les seuls points rationnels sur Q de la courbe X 0 (169) sont les pointes.

En conséquence, il n’existe pas de courbe elliptique définie sur Q possédant un sous-groupe cyclique rationnel d’ordre 13 2 .

We prove that the only rational point of the curve X 0 (169) are the cusps.

Consequently, there does not exist any elliptic curve defined over Q which possesses a rational cyclic subgroup of order 13 2 .

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     author = {Mestre, Jean-Fran\c cois},
     title = {Points rationnels de la courbe modulaire $X\_0(169)$},
     journal = {Annales de l'Institut Fourier},
     volume = {30},
     year = {1980},
     pages = {17-27},
     doi = {10.5802/aif.782},
     mrnumber = {81h:10036},
     zbl = {0432.14017},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1980__30_2_17_0}
}

Mestre, Jean-François. Points rationnels de la courbe modulaire $X_0(169)$. Annales de l'Institut Fourier, Tome 30 (1980) pp. 17-27. doi : 10.5802/aif.782. http://gdmltest.u-ga.fr/item/AIF_1980__30_2_17_0/

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