Ochoa Curve

The Elliptic Curve

$$3Y^2=2X^3+386X^2+256X-58195,$$

given in Weierstraß Form as

$$y^2=x^3-440067x+106074110.$$

The complete set of solutions to this equation consists of $(x,y)=(-761, 504)$, ($-745$, 4520), ($-557$, 13356), ($-446$, 14616), ($-17$, 10656), (91, 8172), (227, 4228), (247, 3528), (271, 2592), (455, 200), (499, 3276), (523, 4356), (530, 4660), (599, 7576), (751, 14112), (1003, 25956), (1862, 75778), (3511, 204552), (5287, 381528), (23527, 3607272), (64507, 16382772), (100102, 31670478), and (1657891, 2134685628) (Stroeker and de Weger 1994).

References

Guy, R. K. ``The Ochoa Curve.'' Crux Math. 16, 65-69, 1990.

Ochoa Melida, J. ``La ecuacion diofántica $b_0y^3-b_1y^2+b_2y-b_3=z^2$.'' Gaceta Math. 139-141, 1978.

Stroeker, R. J. and de Weger, B. M. M. ``On Elliptic Diophantine Equations that Defy Thue's Method: The Case of the Ochoa Curve.'' Experiment. Math. 3, 209-220, 1994.