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curve #1591

y² + xy = x³ − 59867x + 10816849

a-invariants: [1, 0, 0, -59867, 10816849]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 15913354
discriminant (Δ): -36860171634343936
Faltings height: 1.8702
naive height: 45.9173
primes of bad reduction: 2, 31, 43, 47, 127
regulator: 27.18200690871229843458660819285856571684482673
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:23:40 UTC
last updated: 2026-09-25 01:23:40 UTC

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

(-158, -3963)
(124, -2365)
(312, 4591)
(6286/9, -484693/27)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:23:40 UTC · history

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