On the structure of elliptic fields. I
Izvestiya. Mathematics, Tome 27 (1986) no. 1, pp. 39-51
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Let $\mathscr K$ be an algebraic field and $\mathscr F$ an elliptic curve defined over $\mathscr K$. Let $\{O_{p^t},O'_{pt}\}$ be a basis of all the points of order $p^t$ on $\mathscr F$. The field $\mathscr K(O_{p^t},O'_{pt})/\mathscr K(O_p)$ is given explicitly. Bibliography: 3 titles.
@article{IM2_1986_27_1_a2,
author = {V. A. Dem'yanenko},
title = {On the structure of elliptic {fields.~I}},
journal = {Izvestiya. Mathematics},
pages = {39--51},
year = {1986},
volume = {27},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1986_27_1_a2/}
}
V. A. Dem'yanenko. On the structure of elliptic fields. I. Izvestiya. Mathematics, Tome 27 (1986) no. 1, pp. 39-51. http://geodesic.mathdoc.fr/item/IM2_1986_27_1_a2/
[1] Demyanenko V. A., “Kruchenie ellipticheskikh krivykh”, Izv. AN SSSR, Ser. matem., 35:2 (1971), 280–307
[2] Demyanenko V. A., “K sootnosheniyam Abelya”, Zap. nauchn. semin. LOMI, 112, 1983, 58–61 | MR
[3] Demyanenko V. A., “O poryadkakh tochek krucheniya ellipticheskikh krivykh”, Zap. nauchn. semin. LOMI, 112, 1983, 47–57 | MR