curve #3299

y² + xy + y = x³ + x² − 48704x + 4116800

a-invariants: [1, 1, 1, -48704, 4116800]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 59943
discriminant (Δ): 2337777
Faltings height: 1.0579
naive height: 43.9942
primes of bad reduction: 3, 13, 29, 53
regulator: 12.7465379676428973935932554309061460735878
submitted by: David Renshaw
submitted at: 2026-09-26 20:53:52 UTC
last updated: 2026-09-26 20:53:52 UTC

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

(102, 421)
(27, 1666)

Commentary

Cremona 59943h1 = LMFDB 59943.c3: https://www.lmfdb.org/EllipticCurve/Q/59943/c/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 59943, minimal discriminant 2337777, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

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