curve #2845

y² = x³ − x² − 787520x + 269255232

a-invariants: [0, -1, 0, -787520, 269255232]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 305040
discriminant (Δ): 34895795097600
Faltings height: 1.9170
naive height: 52.3435
primes of bad reduction: 2, 3, 5, 31, 41
regulator: 7.8592842061040382364912764268833134072809573
submitted by: David Renshaw
submitted at: 2026-09-26 20:25:02 UTC
last updated: 2026-09-26 20:25:02 UTC

Witness: 3 independent points log in to add more points →

(512, 24)
(514, 50)
(488, 960)

Commentary

Cremona 305040s3 = LMFDB 305040.s1: https://www.lmfdb.org/EllipticCurve/Q/305040/s/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 305040, minimal discriminant 34895795097600, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:25:02 UTC · history