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curve #1288

y² + xy + y = x³ − 1699035153x + 16826142906256

a-invariants: [1, 0, 1, -1699035153, 16826142906256]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 134452649310
discriminant (Δ): 191587426105426102766601562500
Faltings height: 4.3200
naive height: 75.3736
primes of bad reduction: 2, 3, 5, 7, 41, 853, 18307
regulator: 115.410822706130189414789311950034869289957536750
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:26:10 UTC
last updated: 2026-09-24 17:26:10 UTC

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

(9905, 979422)
(10535, 304692)
(36365, 1751172)
(228655, 107510672)
(150530, 56245047)

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 17:26:10 UTC · history

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