Cubic Surfaces Jaap Top - Wiskunde

So it is possible to improve Euler’s result!
parametrizations using cubic polynomials were recently found algebraically
by Noam Elkies and geometrically (using the modern
proof of Clebsch’s theorem above) by Irene Polo and me:
x = −a 3 − 2a 2 c + 3a 2 b + 12abc − 3ab 2 − 4ac 2 + 6b 2 c + 12bc 2 + 9b 3
y = a 3 + 2a 2 c + 3a 2 b + 12abc + 3ab 2 + 4ac 2 − 6b 2 c + 12bc 2 + 9b 3
z = −8c 3 − 8ac 2 − 9b 3 − a 3 − 3a 2 b − 3ab 2 − 4a 2 c − 12b 2 c
w = 8c 3 + 8ac 2 − 9b 3 + a 3 − 3a 2 b + 3ab 2 + 4a 2 c + 12b 2 c.
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