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curve #4066

y² + xy = x³ + 1165886x + 115195619

a-invariants: [1, 0, 0, 1165886, 115195619]
c-invariants: [-55962527, -99445071025]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 943207629
discriminant (Δ): -107148733810456722111
Faltings height: 2.5326
naive height: 53.5206
primes of bad reduction: 3, 7, 13, 29, 109, 1093
regulator: 1092.339802176960129651707205829740945645367834
submitted by: NDElkies
submitted at: 2026-10-09 03:00:37 UTC
last updated: 2026-10-09 03:00:37 UTC

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

(-49, 7637)
(4127, 272204)
(2503, 135556)
(1751, 85877)

Commentary

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

last edited by NDElkies at 2026-10-09 03:00:37 UTC · history

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