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curve #1287

y² + xy = x³ − 187559410x + 3398634755972

a-invariants: [1, 0, 0, -187559410, 3398634755972]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 108997034970
discriminant (Δ): -4567680015838976628288000000
Faltings height: 3.9910
naive height: 71.2319
primes of bad reduction: 2, 3, 5, 37, 997, 98491
regulator: 122.126829022395387514620922556011013213752771271
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:26:00 UTC
last updated: 2026-09-24 17:26:00 UTC

Witness: 5 independent points log in to add more points →

(-19096, -120322)
(34184, -6094342)
(11684, 1668158)
(18644, -2535682)
(-17098, -1259182)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:26:00 UTC · history

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