curve #3265

y² = x³ − x² − 27744x + 1787904

a-invariants: [0, -1, 0, -27744, 1787904]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 816
discriminant (Δ): 110841053184
Faltings height: 1.1937
naive height: 42.3060
primes of bad reduction: 2, 3, 17
regulator: 3.826981769488477113371502881457380599672
submitted by: David Renshaw
submitted at: 2026-09-26 20:48:22 UTC
last updated: 2026-09-26 20:48:22 UTC

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

(146, 910)

Commentary

Cremona 816h3 = LMFDB 816.b2: https://www.lmfdb.org/EllipticCurve/Q/816/b/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 816, minimal discriminant 110841053184, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:48:22 UTC · history