Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census

Sompong Chuysurichay, Sawian Jaidee, Chatchawan Panraksa +1

We record a finite-field census of the split-cubic elliptic curves $E_{a,b,c}^{(n)}:y^2=(ax+n)(bx+n)(cx+n)$ attached to positive integral $D(n)$-triples. For $n\in\{-3,3,5,8,12,20\…