What value on P gives an ellipse with 768 lattice Points? x^2 + 3y^2 = P
P= 4\*7\*13\*19\*31\*37\*43 gives 384 lattice points



How many integer points does my favorite ellipse goes through?
For example, using $P' = P \cdot q$ where $q$ is any of $49,61,67,73,79,97$.


