Torsion and Positive Rank in an Elliptic Family Arising from Cubic 2-Cycles

Sompong Chuysurichay, Sawian Jaidee, Chatchawan Panraksa

We study the elliptic family $E_t:Y^2=X^3+4X^2+16t^2$ arising from rational $2$-cycles of $x^3+bx+a$. For every $t\in {\mathbb{Q}}^{\times }$, we prove that $P_t=(0,-4t)$ has infinite or…