an:03857283
Zbl 0539.14021
Dem'yanenko, V. A.
On Abel's relations
RU
Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 121, 58-61 (1983).
00221101
1983
j
14H45 14H52 14K15 14G25
Abel relations; n-torsion points
For an elliptic curve E given in Weierstrass form, the author derives a relationship among the coordinates of the n-torsion points of E similar to Abel's relations (cf. \textit{H. Weber}, Lehrbuch der Algebra, Vol. 3, {\S}62). The proof uses identities from former work of the author [cf. Mat. Zametki 14, 827-832 (1973; Zbl 0284.14013) and 33, 111-116 (1982; Zbl 0532.14015)]. As a consequence, the author obtains the following: if E and its n-torsion points are defined over an algebraic number field K such that \(12\equiv 0(mod n),\) then \(D^{1/n}\in K,\) where D is the discriminant of E.
G.Angerm??ller
Zbl 0284.14013; Zbl 0532.14015