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curve #4093

y² + xy + y = x³ + x² − 16065x + 714870

a-invariants: [1, 1, 1, -16065, 714870]
c-invariants: [771121, -623431241]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 3018435
discriminant (Δ): 40430158966785
Faltings height: 1.3511
naive height: 40.6668
primes of bad reduction: 3, 5, 7, 17, 19, 89
regulator: 69.248817272265421274999337538995539129095400
submitted by: NDElkies
submitted at: 2026-10-09 14:25:37 UTC
last updated: 2026-10-09 14:25:37 UTC

Witness: 3 independent points log in to add more points →

(114, -675)
(90, 45)
(345, 5859)

Commentary

Second-smallest Faltings height of all curves of naïve height at most 2^90 with this MW group

last edited by NDElkies at 2026-10-09 14:25:37 UTC · history

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