ON THE ELLIPTIC CURVES WITH INFINITE RATIONAL POINTS
If is an elliptic curve defined over then it is an abelian group with identity The set of rational points of E is a subgroup of E. By Mordell’s Theorem, where is the finite torsion subgroup of and r is a non-negative integer. Thus, is infinite if and only if We find a family of elliptic curves with infinitely many rational points.
elliptic curves, Mordell-Weil theorem, torsion group.