Solutions to $y^2 = x^3 + k$?

The equation $y^2 = x^3 + k$ for $k = (4n-1)^3 – 4m^2$, with $m, n \in \mathbb{N}$ and no prime number that p is congruent to 1 modulo 4 divids m, doesn’t have any answer and its proof can be obtained by using quadratic reciprocity law.

Do you know answers of this equation for two or three different values of $k$? In addition, do you know any reference about that?

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