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curve #426

y² + y = x³ + x² − 72x + 210

a-invariants: [0, 1, 1, -72, 210]
rank (lower bound): ≥ 4
torsion subgroup: trivial
conductor (N): 501029
discriminant (Δ): 501029
Faltings height: -0.0950
naive height: 24.4575
primes of bad reduction: 501029
regulator: 3.169423835688372140470345736177453879429513954
submitted by: NDElkies
submitted at: 2026-08-29 18:54:34 UTC
last updated: 2026-08-29 18:54:34 UTC

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

(5, 0)
(4, 1)
(3, 5)
(6, 5)

Commentary

Smallest prime conductor (and second-smallest conductor) of a curve of rank 4.

last edited by NDElkies at 2026-08-29 18:54:34 UTC · history

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