I tried to solve the integer points of $y(y+2)=x^3+(x+3)(x+5)$ by using Sage's command E.integral_points(). Its output was $[(0 : 3 : 1)]$. I tried that $(x,y)=(0,3)$ satisfies my equation. But what does the third number $1$ means in Sage's notation?
2026-03-27 03:59:16.1774583956
What does the $[(0 : 3 : 1)]$ means in Sage.
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It means that it homogenises it and treats it as a curve in projective space.