curve #3061

y² = x³ + x² − 1815520x + 940954100

a-invariants: [0, 1, 0, -1815520, 940954100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 4080
discriminant (Δ): 3746786595840000
Faltings height: 2.1799
naive height: 54.8493
primes of bad reduction: 2, 3, 5, 17
regulator: 2.787974465583163158996294034088007291876
submitted by: David Renshaw
submitted at: 2026-09-26 20:35:27 UTC
last updated: 2026-09-26 20:35:27 UTC

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

(610, 7800)

Commentary

Cremona 4080be7 = LMFDB 4080.ba1: https://www.lmfdb.org/EllipticCurve/Q/4080/ba/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 4080, minimal discriminant 3746786595840000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:35:27 UTC · history