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curve #1669

y² + xy + y = x³ − 5183953425353x + 4511517235850558648

a-invariants: [1, 0, 1, -5183953425353, 4511517235850558648]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 42652114744890
discriminant (Δ): 123022135193636061535001481726756826500
Faltings height: 6.1364
naive height: 99.4434
primes of bad reduction: 2, 3, 5, 7, 17, 29, 31, 37, 43, 8353
regulator: 407.684001355210776932251922431392872880659634469
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:50:19 UTC
last updated: 2026-09-25 02:50:19 UTC

Witness: 5 independent points log in to add more points →

(1967997, 1388832460)
(4177119, 7463917960)
(-2618856, 356790535)
(1881691674/1681, 22953381429830/68921)
(383046876/169, 4608937259155/2197)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:50:19 UTC · history

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