Which elliptic curves over ℚ pack the most rank into the least height?
This site tracks elliptic curves E/ℚ of high Mordell–Weil rank relative to their height — a leaderboard in the spirit of Dujella's rank tables, but ranking by height as well.
Every entry is backed by an explicit list of rational points. We certify a rank lower bound without computing the exact rank: each point is checked to lie on the curve, and their Néron–Tate height-pairing matrix is verified to be positive definite — so the points are independent in E(ℚ), proving rank ≥ the number of points.
Height is the naive height log max(|c4|3, |c6|2).
Leaderboard coming soon — for now, verify a curve below.
Verify a rank lower bound
Give the Weierstrass coefficients and a set of independent rational points. We confirm the points lie on the curve and are linearly independent.