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curve #1584

y² = x³ + x² − 1769x + 24871

a-invariants: [0, 1, 0, -1769, 24871]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 5360768
discriminant (Δ): 74450345984
Faltings height: 0.8165
naive height: 34.0487
primes of bad reduction: 2, 7, 31, 193
regulator: 9.085577082654492814216268268904370878232315299
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:22:30 UTC
last updated: 2026-09-25 01:22:30 UTC

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

(-45, 124)
(3, 140)
(-14, 217)
(141, 1612)

Commentary

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

last edited by Michael Rubinstein at 2026-09-25 01:22:30 UTC · history

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