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curve #2048

y² = x³ − x² − 1500854x + 706937784

a-invariants: [0, -1, 0, -1500854, 706937784]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 168006048
discriminant (Δ): 777980011536189504
Faltings height: 2.3185
naive height: 54.2782
primes of bad reduction: 2, 3, 7, 29, 37, 233
regulator: 793.9200487187712978675013383763882437675051357
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:09:02 UTC
last updated: 2026-09-26 05:09:02 UTC

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

(64289/16, 15615369/64)
(38453/4, -7481565/8)
(43268/49, 2857140/343)
(486308/169, 312307380/2197)

Commentary

2-isogenous partner of curve#1509 (hdeping).

last edited by Steps Unbounded at 2026-09-26 21:52:15 UTC · history

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