Right! So now the count is correct. Le me see what Sage makes of it…
And the output is: Scheme morphism: From: Projective Space of dimension 1 over Rational Field To: Projective Plane Curve over Rational Field defined by x^4 + 2*x^2*y^2 + y^4 + 10*x^2*z^2 - 6*y^2*z^2 + 8*y*z^3 - 3*z^4 ...
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Defn: Defined on coordinates by sending (s : t) to (54*s^4 - 36*s^2*t^2 - 16*s*t^3 - 2*t^4 : -63*s^4 - 84*s^3*t - 26*s^2*t^2 - 20*s*t^3 + t^4 : 45*s^4 - 12*s^3*t + 22*s^2*t^2 + 4*s*t^3 + 5*t^4)
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A final picture: parametric_plot( (2*(27 - 18*t^2 - 8*t^3 - t^4)/(45 - 12*t + 22*t^2 + 4*t^3 + 5*t^4), -(63 + 84*t + 26*t^2 + 20*t^3 - t^4)/(45 - 12*t + 22*t^2 + 4*t^3 + 5*t^4) ), (t,-1e5,1e5), plot_points=1e6)pic.twitter.com/2Wt2w12BBE
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