curve #2996

y² + xy + y = x³ + x² + 140x + 1892

a-invariants: [1, 1, 1, 140, 1892]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 33915
discriminant (Δ): -1628360895
Faltings height: 0.4497
naive height: 28.5515
primes of bad reduction: 3, 5, 7, 17, 19
regulator: 8.81538981697858622529877633059865072305185
submitted by: David Renshaw
submitted at: 2026-09-26 20:32:33 UTC
last updated: 2026-09-26 20:32:33 UTC

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

(0, 43)
(16, 84)

Commentary

Cremona 33915g1 = LMFDB 33915.d4: https://www.lmfdb.org/EllipticCurve/Q/33915/d/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 33915, minimal discriminant -1628360895, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:32:33 UTC · history