5 problems

A Mordell elliptic curve is a curve with Weierstrass form … An $x$- or $y$-arithmetic progression on $E_k$ is an arithmetic progression in the corresponding coordinate. Mohanty's c…

Let $p$ be a prime with $p\equiv 4,7\pmod 9$, and define … Let $E_{2q}$ be the elliptic curve $Y^2=X^3-432(2q)^2$. The BSD parity conjecture. It predicts that … The source explains…

Let $n>2$ be a cube-free integer, and let $E_n$ be the elliptic curve … Write $L(s,E_n)$ for its complex $L$-function and $\operatorname{rank}_{\mathbb Z}E_n(\mathbb Q)$ for its Mo…

Ghadermarzi's rank-1 conjecture. The number of integral points on the quasi-minimal model of $E_B$ is at most $12$.

The sextic-twist height conjecture. For fixed $\epsilon>0$, the set of $d\in S_6(X)\setminus\{0\}$ such that