curve #3157

y² + xy = x³ + x² − 725x − 6375

a-invariants: [1, 1, 0, -725, -6375]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6150
discriminant (Δ): 8510062500
Faltings height: 0.6213
naive height: 31.3743
primes of bad reduction: 2, 3, 5, 41
regulator: 1.71093573707101647340471754658845709444010
submitted by: David Renshaw
submitted at: 2026-09-26 20:40:01 UTC
last updated: 2026-09-26 20:40:01 UTC

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

(35, 95)
(71, 518)

Commentary

Cremona 6150i2 = LMFDB 6150.a2: https://www.lmfdb.org/EllipticCurve/Q/6150/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 6150, minimal discriminant 8510062500, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:40:01 UTC · history