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curve #1721

y² + y = x³ + x² − 133549663269603770x + 19774770656022103186613006

a-invariants: [0, 1, 1, -133549663269603770, 19774770656022103186613006]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 90296038026285
discriminant (Δ): -16486643724513047950060682029660905215239721139196875
Faltings height: 8.7735
naive height: 130.0160
primes of bad reduction: 3, 5, 7, 13, 17, 19, 23, 29, 41, 7489
regulator: 138.633130414957998880711520872548236479564114654
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:15:47 UTC
last updated: 2026-09-25 06:15:47 UTC

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

(53851840, 3569180159317)
(3380270305/16, -63671844122087/64)
(11587282105/16, 1113827122129963/64)
(754063597/4, -9114594545767/8)
(-379366400, 3980080890922)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:15:48 UTC · history

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