curve #1075

y² + xy + y = x³ − 10696531938x + 425805659785156

a-invariants: [1, 0, 1, -10696531938, 425805659785156]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/12ℤ
conductor (N): 99330
discriminant (Δ): 94865985929121315504750000
Faltings height: 4.2980
naive height: 80.8932
primes of bad reduction: 2, 3, 5, 7, 11, 43
regulator: 5.970404849418564998048564126666705160743
submitted by: David Renshaw
submitted at: 2026-09-23 15:25:05 UTC
last updated: 2026-09-23 15:25:05 UTC

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

(193340, 74635287)

Commentary

Cremona 99330bg5 = LMFDB 99330.bg3: https://www.lmfdb.org/EllipticCurve/Q/99330/bg/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 99330, minimal discriminant 94865985929121315504750000, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:25:05 UTC · history