A note on the real Jacobian conjecture in degree 7

Let $(p,q)$ be a Jacobian pair. We show that the real Jacobian conjecture holds if the degree of $p$ is 7 and the highest degree homogenous part is of the form $αx^7 + βx^6y$ for $α^2+β^2 \neq 0$. We then show that there are no atypical Jacobian pairs such that $\mathrm{deg} \, p =7$ and $\mathrm{deg}\, q$ is even and coprime with 7.