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curve #4041

y² + xy + y = x³ + x² − 449x − 1330

a-invariants: [1, 1, 1, -449, -1330]
c-invariants: [21553, 987319]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 12190893
discriminant (Δ): 5229893097
Faltings height: 0.5566
naive height: 29.9348
primes of bad reduction: 3, 11, 13, 157, 181
regulator: 15.83026170824213054991534954472248706822836545
submitted by: NDElkies
submitted at: 2026-10-06 19:18:01 UTC
last updated: 2026-10-06 19:18:01 UTC

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

(-16, 53)
(36, 157)
(49, 287)
(140, 1574)

Commentary

2nd-smallest naïve height for this MW group, by exhaustive search

last edited by NDElkies at 2026-10-06 19:18:01 UTC · history

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