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curve #2051

y² + xy + y = x³ − x² − 837356x − 213199594

a-invariants: [1, -1, 1, -837356, -213199594]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 67158441
discriminant (Δ): 17901206848077859089
Faltings height: 2.4018
naive height: 52.5276
primes of bad reduction: 3, 7, 37, 47, 613
regulator: 858.4620238092345509335929407323901819300564607
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:09:09 UTC
last updated: 2026-09-26 05:09:09 UTC

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

(-716, 4705)
(26844/25, -1463707/125)
(5500, 399162)
(-178671/256, 24189535/4096)

Commentary

2-isogenous partner of curve#1699 (Michael Rubinstein).

last edited by Steps Unbounded at 2026-09-26 21:51:49 UTC · history

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