On the elliptic curve $y^2=x(x^2+p)$ over some certain imaginary quadratic fields

Abstract

In this paper, we will talk about the titled elliptic curve defined over imaginary quadratic fields such as $\mathbb{Q}(\sqrt{-q})$, where $q$ is congruent to 3 modulo 8 and $(p,q)=1$.

arXiv commentthis paper has been withdrawn by the author due to a crucial sign error