curve #3259

y² + xy + y = x³ − 58850x + 5490030

a-invariants: [1, 0, 1, -58850, 5490030]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 9842
discriminant (Δ): 68894
Faltings height: 1.0399
naive height: 44.5618
primes of bad reduction: 2, 7, 19, 37
regulator: 8.01733094423464013497158529164376779267113
submitted by: David Renshaw
submitted at: 2026-09-26 20:47:21 UTC
last updated: 2026-09-26 20:47:21 UTC

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

(122, 299)
(192, 1034)

Commentary

Cremona 9842d1 = LMFDB 9842.a3: https://www.lmfdb.org/EllipticCurve/Q/9842/a/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 9842, minimal discriminant 68894, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:47:21 UTC · history