Preprint
Oct 2026
Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census
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 $n\in\{-3,3,5,8,12,20\}$ there are $164$ such triples with $1\le a<b<c\le100$, allowing zero squares. Their reductions at the ten primes $\operatorname{NextPrime}...
Sompong Chuysurichay, S. Jaidee, Chatchawan Panraksa et al.
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