Elliptic divisibility sequences over certain curves Original Research Article

Let ngreater-or-equal, slanted5 be an integer. We provide an effective method for finding all elliptic curves in short Weierstrass form image with j(E)set membership, variant{0,1728} and all image such that the nth term in the elliptic divisibility sequence defined by P over E fails to have a primitive divisor. In particular, we improve recent results of Everest, Mclaren, and Ward on the Zsigmondy bounds of elliptic divisibility sequences associated with congruent number curves.