curve #2779

y² + xy = x³ − x² − 115x + 225

a-invariants: [1, -1, 0, -115, 225]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 9010
discriminant (Δ): 81180100
Faltings height: 0.2114
naive height: 25.8533
primes of bad reduction: 2, 5, 17, 53
regulator: 2.36225407250349526690972460616404779585717
submitted by: David Renshaw
submitted at: 2026-09-26 20:22:05 UTC
last updated: 2026-09-26 20:22:05 UTC

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

(0, 15)
(20, 65)

Commentary

Cremona 9010a2 = LMFDB 9010.b2: https://www.lmfdb.org/EllipticCurve/Q/9010/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 9010, minimal discriminant 81180100, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:22:06 UTC · history