curve #3050

y² + xy = x³ + 46376x + 5353040

a-invariants: [1, 0, 0, 46376, 5353040]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 7854
discriminant (Δ): -18744614063916048
Faltings height: 1.8074
naive height: 44.5081
primes of bad reduction: 2, 3, 7, 11, 17
regulator: 3.065314620962403031469437299135636909588
submitted by: David Renshaw
submitted at: 2026-09-26 20:34:58 UTC
last updated: 2026-09-26 20:34:58 UTC

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

(86, 3116)

Commentary

Cremona 7854o4 = LMFDB 7854.p5: https://www.lmfdb.org/EllipticCurve/Q/7854/p/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 7854, minimal discriminant -18744614063916048, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:34:58 UTC · history