Infinitely many elliptic curves over $\mathbb{Q}(i)$ of exact ranks 4 and 6 with $j$-invariant 1728

Ben Savoie

For each $r\in \{4,6\}$, we construct an explicit one-parameter family of elliptic curves over $\mathbb{Q}(i)$ containing infinitely many pairwise nonisomorphic curves genuinely def…