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curve #1308

y² = x³ − x² − 3813604608x + 22432138613712

a-invariants: [0, -1, 0, -3813604608, 22432138613712]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 16595089328400
discriminant (Δ): 3332303576792664312863376000000
Faltings height: 4.5477
naive height: 77.7991
primes of bad reduction: 2, 3, 5, 11, 17, 29, 73, 181, 193
regulator: 649.61412447759716244434670360642509037035548754372
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:29:35 UTC
last updated: 2026-09-24 17:29:35 UTC

Witness: 6 independent points log in to add more points →

(-60888, 5375700)
(596142, 457830450)
(-6108, 6745200)
(-58303, 6825500)
(90977/16, 61770775/64)
(122372, 37259200)

Commentary

Torsion Z/2+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 17:29:35 UTC · history

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