curve #2776

y² = x³ − 73x + 72

a-invariants: [0, 0, 0, -73, 72]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 19040
discriminant (Δ): 22657600
Faltings height: 0.1030
naive height: 24.4850
primes of bad reduction: 2, 5, 7, 17
regulator: 3.48392505938217146539182355580682639094515
submitted by: David Renshaw
submitted at: 2026-09-26 20:21:56 UTC
last updated: 2026-09-26 20:21:56 UTC

Witness: 2 independent points log in to add more points →

(-1, 12)
(9, 12)

Commentary

Cremona 19040h1 = LMFDB 19040.b3: https://www.lmfdb.org/EllipticCurve/Q/19040/b/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 19040, minimal discriminant 22657600, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:21:56 UTC · history