curve #2693

y² + xy = x³ − 374x − 2541

a-invariants: [1, 0, 0, -374, -2541]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 759
discriminant (Δ): 627352209
Faltings height: 0.4220
naive height: 29.3865
primes of bad reduction: 3, 11, 23
regulator: 2.983073350512852707175595929097206163060
submitted by: David Renshaw
submitted at: 2026-09-26 20:18:03 UTC
last updated: 2026-09-26 20:18:03 UTC

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

(34, 139)

Commentary

Cremona 759b2 = LMFDB 759.b5: https://www.lmfdb.org/EllipticCurve/Q/759/b/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 759, minimal discriminant 627352209, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:18:03 UTC · history