EUCLIDEAN-LAGRANGE AND CANTOR-LAGRANGE QUARTIC POLYNOMIALS AND ASSOCIATED CUBIC CURVES

The purpose of this paper is to introduce and examine two classes of quartic real polynomials P having the same Euclidean norm as their Lagrange resolvent, respectively, having the square of the Euclidean norm equal to the height of the Lagrange resolvent. The reduced form of the polynomial P is provided, which eliminates the cubic term. Find ing such polynomials with integer coefficients is always of interest. The Lagrange resolvent associates a cubic curve with each of these polyno mials as a cubic polynomial. It highlights the situations in which these cubic curves are elliptic curves.