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Points are represented using projective coordinates, a common tool to work with curves. Most standard references for elliptic curves will mention them. You can see:

sage: e = EllipticCurve(GF(13),[0,1])
sage: e.defining_polynomial()
-x^3 + y^2*z - z^3

If we set (x,y,z)=(X,Y,1) we get the equation Y^2=X^3+1, which is probably the model you were expecting. An additional solution is (x,y,z)=(0,1,0). That's the "extra point at infinity" that is the identity for the standard group law on an elliptic curve given by an equation of this form.