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ALGEBRAIC POINTS OF GIVEN DEGREE ON THE AFFINE CURVE $C : y^2 = x^5 + 16$
Keywords:
planes curves, degree of algebraic points, rational points, algebraic extensions, JacobianAbstract
In this work, we determine the set of algebraic points of a given degree over $\mathbb{Q}$ on the curve of affine equation $y^2 = x^2 + 4^2$. This note extends a result of Mulholland in [8] who gave a description of the set of $\mathbb{Q}$-rational points, i.e., the set of points of degree one over $\mathbb{Q}$ on this curve.
Received: February 20, 2022
Accepted: March 29, 2022
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