Explore the intricate relationship between the heights of algebraic cycles and special values of L-series in this comprehensive conference talk. Delve into the examination of CM points on elliptic curves and Gross—Schoen cycles on triple products of elliptic curves. Gain insights from the collaborative work in progress by Shou-Wu Zhang, Xinyi Yuan, and Wei Zhang, along with significant contributions from Yifeng Liu. Discover the latest advancements in algebraic geometry and number theory as presented at the International Congress of Basic Science (ICBS) 2024.