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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 $K=\mathbb{Q}(\sqrt{-2})$. How can I compute the $K$-rational points on the modular curve $X_0(35)$? Recall that $X_0(35)$ is a hyperelliptic curve of genus 3 and has the simplified affine model: \...