E=EllipticCurve([0,-82569375])
E.integral_points()
[(436 : 559 : 1), (450 : 2925 : 1), (666 : 14589 : 1), (900 : 25425 :1),
(1150 : 37925 : 1), (1800 : 75825 : 1), (2619 : 133722 : 1), (26154:
4229667 : 1), (27675 : 4603950 : 1)]
What about 748476100^3-82569375 = 20477027135825^2
Best wishes
Artur
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