Geodesic
On the division by an isogeny of the points of an elliptic curve
Sbornik. Mathematics, Tome 22 (1974) no. 3, pp. 473-492

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In the first part of this article we investigate the field of definition of the group $\nu^{-1}(E(K))$, where $\nu$ is an isogeny of degree $\rho$ of an elliptic curve $E$ over a local field $K$, with $[K:\mathbf Q_p]\infty$. In the second part we show that local results have global consequences for various elliptic curves with complex multiplication. They are concerned with describing groups of rational points of Shafarevich–Tate groups and Mazur modules over $\Gamma$-extensions. Bibliography: 16 titles. 
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     author = {V. G. Berkovich},
     title = {On the division by an isogeny of the points of an elliptic curve},
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V. G. Berkovich. On the division by an isogeny of the points of an elliptic curve. Sbornik. Mathematics, Tome 22 (1974) no. 3, pp. 473-492. http://geodesic.mathdoc.fr/item/SM_1974_22_3_a8/