All Questions

Let $C$ be an affine curve given by $p_C(x,y)=0$ where $$ p_C=2x^3y + 2xy^3 +x^3 + y^3 + 5x^2y + 5xy^2 + 2x^2 + 2y^2 + 2x^2y^2 + 2xy $$ and let $\overline{C}$ denote the projective closure of $C$. For ...

Let $f \in \mathbb Q[x]$ be a squarefree cubic polynomial with nonzero constant coefficient and consider the elliptic curve $E : y^2 = f(x)$. Define $E(\mathbb Q)' \subseteq E(\mathbb Q)$ as $$\left \...

Suppose we consider a arbitrary cubic homogeneous form $f$ in in four or five variables over the rational field. Is there any computational tool or algorithm to check whether this cubic homogeneous ...