Algebraic Points of Any Degree on the Affine Curve \(y^{2}=3x(x^{4}+3)\)

We determine the set of algebraic points of any degree over \(\mathbb {Q}\) on the affine curve \(y^{2}=3x(x^{4}+3).\) This result generalize the previous respective results of Bruin who described in Bruin (On powers as sums of two cubes. In: International Algorithmic Number Theory Symposium. Springer, Berlin, 2000) the set of \(\mathbb {Q}\) -rationals points and of Sow, Sarr and Sall who described in Sow et al. (Int J Develop Res 11(12): 52435–52439, 2021) the set of algebraic points of degree at most 5 over \(\mathbb {Q}\) on this curve.