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curve #2039

y² + xy = x³ + x² − 33616172125x + 2371261996478125

a-invariants: [1, 1, 0, -33616172125, 2371261996478125]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 9680213412150
discriminant (Δ): 2108396963357296779771506250000
Faltings height: 4.7712
naive height: 84.3284
primes of bad reduction: 2, 3, 5, 41, 61, 101, 449, 569
regulator: 645505.41160931925591604919252018105719070464624838
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:06:07 UTC
last updated: 2026-09-26 05:06:07 UTC

Witness: 6 independent points log in to add more points →

(363131, 194878178)
(13062019/121, -886646119/1331)
(8220739/49, 13048956094/343)
(42111350/289, -117327048725/4913)
(155171350/1089, 780127380475/35937)
(3623298850/33489, -5534260728775/6128487)

Commentary

2-isogenous partner of curve#1687 (Michael Rubinstein).

last edited by Steps Unbounded at 2026-09-26 21:49:22 UTC · history

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