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curve #4092

y² + xy = x³ − 14209x + 749840

a-invariants: [1, 0, 0, -14209, 749840]
c-invariants: [682033, -648884809]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 2131311
discriminant (Δ): -60064165420623
Faltings height: 1.3679
naive height: 40.5815
primes of bad reduction: 3, 7, 13, 37, 211
regulator: 78.999206700739668170976978872631178815146734
submitted by: NDElkies
submitted at: 2026-10-09 14:21:31 UTC
last updated: 2026-10-09 14:21:31 UTC

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

(116, 758)
(-19, 1016)
(701, 17963)

Commentary

Third-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 14:21:31 UTC · history

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