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curve #1560

y² + xy = x³ − 2586270940000x + 1603563138320000000

a-invariants: [1, 0, 0, -2586270940000, 1603563138320000000]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/7ℤ
conductor (N): 681955890
discriminant (Δ): -3712760084559933236106196254720000000
Faltings height: 5.9059
naive height: 97.3607
primes of bad reduction: 2, 3, 5, 7, 11, 295219
regulator: 16.287699850837494907861785100431905436999488
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:05:49 UTC
last updated: 2026-09-25 01:05:49 UTC

Witness: 3 independent points log in to add more points →

(133100, 1123182500)
(3690500, 6503750000)
(1022450, 167131250)

Commentary

Torsion Z/7. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:05:50 UTC · history

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