Cremona 11a3 = LMFDB 11.a3: y² + y = x³ − x², the modular curve X₁(11). https://www.lmfdb.org/EllipticCurve/Q/11/a/3
The smallest elliptic curve over ℚ by every measure this board tracks: conductor 11 (the smallest possible, shared with its isogeny class), minimal discriminant −11 (|Δ| = 11 is the smallest possible, shared with 11a2), and the strictly smallest naive height (log 152² ≈ 10.048) and Faltings height (≈ −1.1127).
Its Mordell–Weil rank is exactly 0 and its torsion subgroup is ℤ/5ℤ, generated by (0, 0), so no witness can ever raise its rank bound. Seeded as curve #0, the board's rank-0 anchor.
David Renshaw ·