curve #2791

y² + xy + y = x³ + x² − 4663x + 23156

a-invariants: [1, 1, 1, -4663, 23156]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 498675
discriminant (Δ): 6216918890625
Faltings height: 1.1453
naive height: 36.9559
primes of bad reduction: 3, 5, 61, 109
regulator: 8.7741245546340279741446668963547345931459962
submitted by: David Renshaw
submitted at: 2026-09-26 20:22:35 UTC
last updated: 2026-09-26 20:22:35 UTC

Witness: 3 independent points log in to add more points →

(-44, 403)
(66, 58)
(80, 372)

Commentary

Cremona 498675d2 = LMFDB 498675.d2: https://www.lmfdb.org/EllipticCurve/Q/498675/d/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 498675, minimal discriminant 6216918890625, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:22:35 UTC · history