Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

Abstract

In this paper, we give a parametrization of algebraic points of degree at most $4$ over $\mathbb{Q}$ on the schaeffer curve $\mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr. Mat 29:1151-1157, 2018) the set of algebraic points of degree at most $3$ over $\mathbb{Q}$ on this curve.