# Diophantine symmetric quadratic system

Take a box $$mathcal B subseteq mathbb Z ^ 8$$ around the origin of the same side lenth $$ell$$. What is the minimum $$ell$$ need for the following system quadratic polynomials to have a solution $$mathcal B$$

$$wz + xy = w & z; + x & # 39; y & # 39; = wz + xy & # 39; = w + x + y = 0$$
with $$| wx | neq | yz | neq | w & # 39; x & # 39; neq | There & # 39; z & # 39; |$$?