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curve #4049

y² = x³ − x² − 3400607889x + 62934590972529

a-invariants: [0, -1, 0, -3400607889, 62934590972529]
c-invariants: [163229178688, -54374507225192960]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5829048278592
discriminant (Δ): 805817595730852196893536436224
Faltings height: 4.4567
naive height: 77.4553
primes of bad reduction: 2, 3, 7, 11, 67, 79, 163, 457
regulator: 894.96483351030331431544602313490956585132909559445
submitted by: Michael Rubinstein
submitted at: 2026-10-07 22:24:24 UTC
last updated: 2026-10-07 22:24:24 UTC

Witness: 6 independent points log in to add more points →

(-1131, 8171856)
(8504, 5884789)
(5961325/9, 14500120096/27)
(90729491/289, 850069540628/4913)
(-24925329/529, 132478369968/12167)
(312219/25, 591778572/125)

Commentary

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

last edited by Michael Rubinstein at 2026-10-07 22:24:24 UTC · history

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