Geodesic
Some remarks on the torsion of elliptic curves
Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 283-289 
M. E. Novodvorskii; I. I. Pyatetskii-Shapiro. Some remarks on the torsion of elliptic curves. Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 283-289. http://geodesic.mathdoc.fr/item/SM_1970_11_2_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the following. Theorem. {\it Let $k$ be a number field, and $J(n)$ the Jacobian of the curve parametrizing the elliptic curves with distinguished cyclic subgroups of order $n$. If the number $N$ is written as $n\cdot a,$ where $J(a)$ contains a $k$-simple abelian subvariety $A$ such that $$ \tau(n)\times\operatorname{rk}\operatorname{End}_k(A)>\operatorname{rk}A_k, $$ then the set of $k$-isomorphism classes of elliptic curves over the field $k$ possessing $k$-points of order $N$ is finite}. Bibliography: 4 titles.

[1] Yu. I. Manin, “$p$-kruchenie ellipticheskikh krivykh ravnomerno ogranicheno”, Izv. AN SSSR, seriya matem., 33:3 (1969), 459–466 | MR

[2] I. M. Gelfand, M. I. Graev, I. I. Pyatetskii-Shapiro, Teoriya predstavlenii i avtomorfnye funktsii, Nauka, Moskva, 1966 | MR

[3] D zh. Kassels, “Diofantovy uravneniya so spetsialnym rassmotreniem ellipticheskikh krivykh. I”, Matematika, 12:1 (1968), 111–160

[4] Y. Ihara, On congruence monodromy problems, v. 1, Lecture Notes, Department of Mathematics, University of Tokyo, Tokyo, 1968 | MR | Zbl