\(n\)-universal quadratic forms, quadratic ideals and elliptic curves over finite fields (Q2891120)

Section 1 contains preliminaries about integral binary quadratic forms.NEWLINENEWLINE In section 2 the authors make some elementary observations on the properties of the quadratic form \(x^2+5xy+6y^2\).NEWLINENEWLINE In section 3 they study the quadratic form \(-x^2+4xy-4y^2\) over finite prime fields. Their efforts could have lessend by observing that the form has shape \(-(x-2y)^2\). For instance, the 22 statements of Theorem 3.5 about conditions under which the form represents \(\pm a\), for \(a=1,\ldots ,10\), become a triviality.NEWLINENEWLINE The last section is devoted to calculation of the number of points on the cubic curve \(y^2=x^3-2x^2\) over a finite prime field. Contrary to the announcement in the title, there are no results about elliptic curves in the paper.