curve #3240

y² + xy = x³ − 433x + 3432

a-invariants: [1, 0, 0, -433, 3432]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 103525
discriminant (Δ): 517625
Faltings height: 0.1598
naive height: 29.8260
primes of bad reduction: 5, 41, 101
regulator: 5.1502060304058257200075541878505665427029567
submitted by: David Renshaw
submitted at: 2026-09-26 20:44:15 UTC
last updated: 2026-09-26 20:44:15 UTC

Witness: 3 independent points log in to add more points →

(11, 0)
(13, 0)
(3, 45)

Commentary

Cremona 103525c1 = LMFDB 103525.a2: https://www.lmfdb.org/EllipticCurve/Q/103525/a/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 103525, minimal discriminant 517625, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:44:15 UTC · history