I am trying to find integer points $(x,y)$ on the elliptic curve $$y^2=x^3-4x+9$$ Is there an elementary way to calculate all the solutions?

I have brute-forced solutions for $(x,y)$ under $1000$ and only $(2,3), (7,18), (11,36)$ seem to work. Does someone have a theoretical way of checking for all the solutions, or otherwise a Sage code would be appreciated?