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curve #1589

y² + xy = x³ − x² − 4398x + 113120

a-invariants: [1, -1, 0, -4398, 113120]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 7814358
discriminant (Δ): 24052593924
Faltings height: 0.8683
naive height: 36.7804
primes of bad reduction: 2, 3, 19, 73, 313
regulator: 8.471260420172846097260838984157343578070569486
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:23:20 UTC
last updated: 2026-09-25 01:23:20 UTC

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

(-17, 436)
(97, 721)
(-74, 208)
(103/4, 923/8)

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 01:23:20 UTC · history

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