curve #2947

y² + y = x³ + 90

a-invariants: [0, 0, 1, 0, 90]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 9747
discriminant (Δ): -3518667
Faltings height: -0.0650
naive height: 22.5283
primes of bad reduction: 3, 19
regulator: 7.19459159982179587326343538683724463630458
submitted by: David Renshaw
submitted at: 2026-09-26 20:29:37 UTC
last updated: 2026-09-26 20:29:37 UTC

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

(6, 17)
(-15/4, 45/8)

Commentary

Cremona 9747f1 = LMFDB 9747.d2: https://www.lmfdb.org/EllipticCurve/Q/9747/d/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 9747, minimal discriminant -3518667, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:29:37 UTC · history