EXIBITION PRAMETRIC FAMILY OF ALGEBRIC POINTS OF GIVEN DEGREE ON THE AFFINE EQUATION CURVE: −y2 = x6 − 20x3 − 8

Abstract

We give an explicit parametric family of algebraic points of given degree on Q over the affine equation curve: -y² = x⁶ - 20x³ - 8. These curves are described by Nils BRUIN in [1], who showed that the MordellWeill group is finite and explained the generators of the torsion group for this curve.