curve #3293

y² + xy + y = x³ + x² − 305x + 4502

a-invariants: [1, 1, 1, -305, 4502]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 57855
discriminant (Δ): -7441599375
Faltings height: 0.5824
naive height: 30.4035
primes of bad reduction: 3, 5, 7, 19, 29
regulator: 2.59679098815781680378950072846032755807474
submitted by: David Renshaw
submitted at: 2026-09-26 20:52:53 UTC
last updated: 2026-09-26 20:52:53 UTC

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

(2, 61)
(5, 53)

Commentary

Cremona 57855i1 = LMFDB 57855.d4: https://www.lmfdb.org/EllipticCurve/Q/57855/d/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 57855, minimal discriminant -7441599375, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:52:53 UTC · history