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curve #4114

y² + xy + y = x³ − x² − 174924457x + 889700154456

a-invariants: [1, -1, 1, -174924457, 889700154456]
c-invariants: [8396373921, -768663149767569]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 92189967815
discriminant (Δ): 632942754580505534707025
Faltings height: 3.4833 ☆ record for ℤ/4ℤ torsion, rank ≥ 5
naive height: 68.5532
primes of bad reduction: 5, 11, 53, 89, 269, 1321
regulator: 1771.00530788504838770308111982124225972228989601
submitted by: NDElkies
submitted at: 2026-10-09 15:30:00 UTC
last updated: 2026-10-09 15:30:00 UTC

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

(8364, 103964)
(57931/4, -9503063/8)
(7341, -37551)
(6934, -104101)
(114349, -38476831)

Commentary

Second-smallest naïve height H, and smallest |D| and Faltings height, of the 5 curves with H < 2^100 and this MW group.

last edited by NDElkies at 2026-10-09 15:36:40 UTC · history

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