curve #3220

y² + xy + y = x³ + x² − x + 14

a-invariants: [1, 1, 1, -1, 14]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 4845
discriminant (Δ): -92055
Faltings height: -0.3684
naive height: 18.8856
primes of bad reduction: 3, 5, 17, 19
regulator: 1.85691246761095834313055635623809874641220
submitted by: David Renshaw
submitted at: 2026-09-26 20:43:17 UTC
last updated: 2026-09-26 20:43:17 UTC

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

(1, 3)
(-2, 4)

Commentary

Cremona 4845c1 = LMFDB 4845.a2: https://www.lmfdb.org/EllipticCurve/Q/4845/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 4845, minimal discriminant -92055, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:43:17 UTC · history