Elliptic curves of twin-primes over Gauss field and Diophantine Equations

DeRong Qiu, Xianke Zhang

Let $p,q$ be twin prime numbers with $q-p=2$ . Consider the elliptic curves E=E_σ: y^2 = x (x+σp)(x+σq) . (σ=\pm 1). E=E_σis also denoted as E_+ or E_- when σ= +1or $-1.Here the M…