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curve #4040

y² = x³ + x² − 895x + 130929

a-invariants: [0, 1, 0, -895, 130929]
c-invariants: [42976, -113380480]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 846118016
discriminant (Δ): -7393379223808
Faltings height: 1.1489
naive height: 37.0925 ☆ record for ℤ/2ℤ torsion, rank ≥ 5
primes of bad reduction: 2, 17, 89, 257
regulator: 129.669960038072202551098290657531365784302364751
submitted by: NDElkies
submitted at: 2026-10-06 19:09:18 UTC
last updated: 2026-10-06 19:09:18 UTC

Witness: 5 independent points log in to add more points →

(-23, 374)
(-40, 323)
(79, 748)
(96, 969)
(15, 348)

Commentary

smallest naïve height for this MW group, by exhaustive search

last edited by NDElkies at 2026-10-06 19:09:18 UTC · history

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