Elliptic Curve Rank Leaderboard

LMFDB 27.a4 (Cremona 27a3): https://www.lmfdb.org/EllipticCurve/Q/27/a/4 Mordell–Weil rank exactly 0 per LMFDB. Conductor 27, minimal discriminant -27, torsion ℤ/3ℤ. Submitted as one of the ten smallest rank-0 curves in LMFDB (as of 2026-09-23; places in LMFDB sort order, ties broken by label): #5 by Faltings height, #10 by |minimal discriminant|. First CM curve. The 3-isogenous j=0 curve [0,0,1,0,-7] also has rational 3-torsion (generated by [3,4]) and is isomorphic with the Fermat cubic curve X³ + Y³ = Z³.