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curve #1289

y² + xy + y = x³ − x² − 196513427x + 1051732985779

a-invariants: [1, -1, 1, -196513427, 1051732985779]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 151198811190
discriminant (Δ): 7878381911443344494592000
Faltings height: 3.5982
naive height: 68.9023
primes of bad reduction: 2, 3, 5, 7, 29, 306511
regulator: 81.6280622462607910155593215114475662784819694368
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:26:21 UTC
last updated: 2026-09-24 17:26:21 UTC

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

(2147, 798746)
(-1493, 1159106)
(6907, 151106)
(7019, 131282)
(59923/9, 5204342/27)

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 17:26:21 UTC · history

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