6 problems

Quadratic isogenies conjecture. There exists an integer $C$, independent of $K$, such that if $N>C$, then every point

Sporadic quadratic-point conjecture. Ranging over all $X_0(N)$ for $N\in{\mathbb Z}_{\ge 1}$, there are only finitely many sporadic quadratic points.

Quadratic-points family conjecture. There is an infinite family $\mathcal{E}\subseteq\widetilde{\mathcal{M}_3^{\operatorname{Pl}}}(G)$ of $\mathbb{Q}$-isomorphism classes of smooth…

Quadratic-points stratum conjecture. There exist subsets $\mathcal{E}$ and $\mathcal{D}$, each of infinite cardinality, such that every member of $\mathcal{E}$ has finitely many qu…

Carathéodory conjecture for quadratic points. Every compact convex surface in $\mathbb{P}^3$ has at least $2$ quadratic points, without assuming that the cubic forms at the quadrat…

Tabach's conjecture. Every hyperbolic torus in $\mathbb{P}^3$ has a quadratic point.