curve #2838

y² + xy + y = x³ + x² − 66240x + 5638272

a-invariants: [1, 1, 1, -66240, 5638272]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 21945
discriminant (Δ): 4733106325880625
Faltings height: 1.7326
naive height: 44.9167
primes of bad reduction: 3, 5, 7, 11, 19
regulator: 2.75124709237994393042223779745915640788859
submitted by: David Renshaw
submitted at: 2026-09-26 20:24:43 UTC
last updated: 2026-09-26 20:24:43 UTC

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

(92, 531)
(22, 2036)

Commentary

Cremona 21945l2 = LMFDB 21945.l4: https://www.lmfdb.org/EllipticCurve/Q/21945/l/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 21945, minimal discriminant 4733106325880625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:24:43 UTC · history