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curve #1689

y² = x³ − x² − 440616033x + 64693411091937

a-invariants: [0, -1, 0, -440616033, 64693411091937]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 18648177600
discriminant (Δ): -1802539657332277557258240000000
Faltings height: 4.4849
naive height: 77.1245
primes of bad reduction: 2, 3, 5, 13, 37, 41, 197
regulator: 376.235235282628468090527488609719108214270729612
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:10:28 UTC
last updated: 2026-09-25 06:10:28 UTC

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

(7053/4, 63960975/8)
(726009/49, 2688066576/343)
(2828073, 4755810096)
(5552163/529, 95202357900/12167)
(3881, 7939888)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:10:28 UTC · history

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