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curve #1608

y² + xy + y = x³ − x² − 28142616137x + 1987967019369161

a-invariants: [1, -1, 1, -28142616137, 1987967019369161]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 1317390570
discriminant (Δ): -280752223558388100824712609792000
Faltings height: 4.9630
naive height: 83.9749
primes of bad reduction: 2, 3, 5, 31, 43, 79, 139
regulator: 63.40840226037998172388202008042309394912504199
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:30:56 UTC
last updated: 2026-09-25 01:30:56 UTC

Witness: 4 independent points log in to add more points →

(89991, 13525564)
(4531389/49, 4538141182/343)
(1626351, 2062665244)
(-16959, 49610494)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:30:56 UTC · history

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