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curve #2052

y² + xy + y = x³ + x² − 3156938x + 2149966406

a-invariants: [1, 1, 1, -3156938, 2149966406]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 50457675
discriminant (Δ): 14321120436031640625
Faltings height: 2.5311
naive height: 56.5089
primes of bad reduction: 3, 5, 41, 61, 269
regulator: 925.5998757915423047072332313704647843139321813
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:09:11 UTC
last updated: 2026-09-26 05:09:11 UTC

Witness: 4 independent points log in to add more points →

(3576, 189538)
(6016, -451267)
(47200, -10271038)
(3088825/256, -5397798523/4096)

Commentary

2-isogenous partner of curve#1601 (Michael Rubinstein).

last edited by Steps Unbounded at 2026-09-26 21:52:40 UTC · history

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