curve #2719

y² + xy = x³ − 11764x + 95888

a-invariants: [1, 0, 0, -11764, 95888]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 4074
discriminant (Δ): 100141447053312
Faltings height: 1.3768
naive height: 39.7320
primes of bad reduction: 2, 3, 7, 97
regulator: 1.334530946710411858526666866257105810724
submitted by: David Renshaw
submitted at: 2026-09-26 20:19:11 UTC
last updated: 2026-09-26 20:19:11 UTC

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

(8, 44)

Commentary

Cremona 4074l1 = LMFDB 4074.k6: https://www.lmfdb.org/EllipticCurve/Q/4074/k/6 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 4074, minimal discriminant 100141447053312, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:19:12 UTC · history