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curve #4065

y² + xy = x³ + 1598846x + 6881343029

a-invariants: [1, 0, 0, 1598846, 6881343029]
c-invariants: [-76744607, -5945365260145]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 31433727 ☆ record for ℤ/4ℤ torsion, rank ≥ 4
discriminant (Δ): -20717230006770760159281
Faltings height: 2.9619
naive height: 58.8273
primes of bad reduction: 3, 13, 61, 73, 181
regulator: 82.21451890005336409216640159335793293277437660
submitted by: NDElkies
submitted at: 2026-10-09 02:53:45 UTC
last updated: 2026-10-09 02:53:45 UTC

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

(-1075, 63152)
(5516, 425657)
(3319, 219139)
(-1460, 38617)

Commentary

smallest conductor of an elliptic curve with this MW group and naïve height at most 2^90

last edited by NDElkies at 2026-10-09 02:53:45 UTC · history

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