# zbMATH — the first resource for mathematics

On Abel’s relations. (Russian) Zbl 0539.14021
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. H. Weber, Lehrbuch der Algebra, Vol. 3, §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.
Reviewer: G.Angermüller

##### MSC:
 14H45 Special algebraic curves and curves of low genus 14H52 Elliptic curves 14K15 Arithmetic ground fields for abelian varieties 14G25 Global ground fields in algebraic geometry
##### Keywords:
Abel relations; n-torsion points
Full Text: