curve #2918

y² + xy + y = x³ − 27x + 50

a-invariants: [1, 0, 1, -27, 50]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 2482
discriminant (Δ): 4964
Faltings height: -0.4118
naive height: 21.4474
primes of bad reduction: 2, 17, 73
regulator: 0.953828004191184730480698477888079639392113
submitted by: David Renshaw
submitted at: 2026-09-26 20:28:19 UTC
last updated: 2026-09-26 20:28:19 UTC

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

(1, 4)
(5, 4)

Commentary

Cremona 2482c1 = LMFDB 2482.a2: https://www.lmfdb.org/EllipticCurve/Q/2482/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2482, minimal discriminant 4964, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:28:20 UTC · history