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curve #1652

y² + xy + y = x³ − x² + 44067370x + 999488807372

a-invariants: [1, -1, 1, 44067370, 999488807372]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 41419028475
discriminant (Δ): -437044812914183389314609375
Faltings height: 3.7916
naive height: 68.7842
primes of bad reduction: 3, 5, 11, 23, 47, 113, 137
regulator: 369.382143411083152420485194584344016778637293883
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:27:24 UTC
last updated: 2026-09-25 02:27:24 UTC

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

(1188, 1025815)
(15765/16, 65357047/64)
(-1029/4, 7953425/8)
(-6816, 621820)
(774, 1016500)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:27:24 UTC · history

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