curve #1040

y² + xy + y = x³ + x² − 17714x + 900047

a-invariants: [1, 1, 1, -17714, 900047]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 966 ☆ record for ℤ/8ℤ torsion, rank ≥ 1
discriminant (Δ): 19093020912 ☆ record for ℤ/8ℤ torsion, rank ≥ 1
Faltings height: 1.0694 ☆ record for ℤ/8ℤ torsion, rank ≥ 1
naive height: 40.9599
primes of bad reduction: 2, 3, 7, 23
regulator: 2.429046614030699609497398526925843435269
submitted by: David Renshaw
submitted at: 2026-09-23 15:19:42 UTC
last updated: 2026-09-23 15:19:42 UTC

Witness: 1 independent point log in to add more points →

(79, -1)

Commentary

Cremona 966g4 = LMFDB 966.g2: https://www.lmfdb.org/EllipticCurve/Q/966/g/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 966, minimal discriminant 19093020912, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:19:42 UTC · history