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curve #1346

y² = x³ − x² − 3134341640x + 67528477424016

a-invariants: [0, -1, 0, -3134341640, 67528477424016]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 28330377346942896
discriminant (Δ): 792790676205854957438257152
Faltings height: 4.1522
naive height: 77.2107
primes of bad reduction: 2, 3, 17, 47, 53, 89, 101, 223, 409
regulator: 20695.3822687685902012221902204774081088598676857597227
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:36:07 UTC
last updated: 2026-09-24 17:36:07 UTC

Witness: 8 independent points log in to add more points →

(36488, 1319268)
(22216, 2976604)
(33496, 348364)
(28906, 1038734)
(32744, -60348)
(210874, -93721102)
(283792/9, 5827436/27)
(38384, -1941852)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:36:07 UTC · history

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