curve #3183

y² + xy = x³ + x² − 204250x + 22562500

a-invariants: [1, 1, 0, -204250, 22562500]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 344850
discriminant (Δ): 323763845006250000
Faltings height: 2.0618
naive height: 48.2949
primes of bad reduction: 2, 3, 5, 11, 19
regulator: 5.7628604225632419419723762837766849809436765
submitted by: David Renshaw
submitted at: 2026-09-26 20:41:18 UTC
last updated: 2026-09-26 20:41:18 UTC

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

(0, 4750)
(400, 2050)
(391, 1438)

Commentary

Cremona 344850c2 = LMFDB 344850.c3: https://www.lmfdb.org/EllipticCurve/Q/344850/c/3 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 344850, minimal discriminant 323763845006250000, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:41:18 UTC · history