curve #3301

y² + xy + y = x³ + x² − 287215x + 59126300

a-invariants: [1, 1, 1, -287215, 59126300]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 226005
discriminant (Δ): 13786305
Faltings height: 1.4445
naive height: 49.3176
primes of bad reduction: 3, 5, 13, 19, 61
regulator: 56.5445426178914001589187972277944433346176
submitted by: David Renshaw
submitted at: 2026-09-26 20:54:11 UTC
last updated: 2026-09-26 20:54:11 UTC

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

(3070/9, 22250/27)
(112485/49, 36394987/343)

Commentary

Cremona 226005g1 = LMFDB 226005.b4: https://www.lmfdb.org/EllipticCurve/Q/226005/b/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 226005, minimal discriminant 13786305, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:54:11 UTC · history