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curve #2050

y² = x³ − 1891731x + 989132690

a-invariants: [0, 0, 0, -1891731, 989132690]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 90471312
discriminant (Δ): 10607835550321741824
Faltings height: 2.4554
naive height: 54.9726
primes of bad reduction: 2, 3, 19, 43, 769
regulator: 982.8686735949589147073298866987002792588062535
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:09:06 UTC
last updated: 2026-09-26 05:09:06 UTC

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

(1682, 50654)
(8465, -769120)
(26002, -4187106)
(34577, -6424544)

Commentary

2-isogenous partner of curve#1512 (hdeping).

last edited by Steps Unbounded at 2026-09-26 21:52:28 UTC · history

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