curve #3273

y² + xy + y = x³ + x² − 287220x + 59124132

a-invariants: [1, 1, 1, -287220, 59124132]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 226005
discriminant (Δ): 190062205553025
Faltings height: 1.7910
naive height: 49.3176
primes of bad reduction: 3, 5, 13, 19, 61
regulator: 14.1361356544728500397296993069486108336544
submitted by: David Renshaw
submitted at: 2026-09-26 20:49:39 UTC
last updated: 2026-09-26 20:49:39 UTC

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

(320, 171)
(432, 3771)

Commentary

Cremona 226005g2 = LMFDB 226005.b3: https://www.lmfdb.org/EllipticCurve/Q/226005/b/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 226005, minimal discriminant 190062205553025, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:49:39 UTC · history