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curve #1270

y² = x³ + x² − 538960x + 188850900

a-invariants: [0, 1, 0, -538960, 188850900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 1565566960
discriminant (Δ): -5416861681600000000
Faltings height: 2.3080
naive height: 51.6380
primes of bad reduction: 2, 5, 31, 41, 89, 173
regulator: 66.9913181267793437683927098106008551290843537354
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:16:16 UTC
last updated: 2026-09-24 17:16:16 UTC

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(130, 11000)
(380, 6250)
(730, 13600)
(1130, 32000)
(-470, 18400)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:16:16 UTC · history

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