curve #424

y² + y = x³ + x²

a-invariants: [0, 1, 1, 0, 0]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 43
discriminant (Δ): -43
Faltings height: -1.0044 ★ record for rank ≥ 1
naive height: 11.2696 ★ record for rank ≥ 1
primes of bad reduction: 43
regulator: 0.06281650708748764926570879146696868631899
submitted by: NDElkies
submitted at: 2026-08-29 17:25:22 UTC
last updated: 2026-08-29 17:25:22 UTC

Witness: 1 independent point log in to add more points →

(0, 0)

Commentary

The second elliptic curve of positive rank (LMFDB 43.a1, a.k.a. the Fricke quotient of the modular curve X_0(43)), which happens to have a somewhat smaller naive height than the rank-1 curve of conductor 37.

last edited by NDElkies at 2026-08-29 17:25:22 UTC · history