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curve #4430

y² + y = x³ − 173137x + 43783716

a-invariants: [0, 0, 1, -173137, 43783716]
c-invariants: [8310576, -37829130840]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 495988201329671483
discriminant (Δ): -495988201329671483
Faltings height: 2.0929
naive height: 48.7127
primes of bad reduction: 49069, 53051, 190533157
regulator: 132771.07224018581216762527750388424408348147994190665646
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:36 UTC
last updated: 2026-10-17 10:23:36 UTC

Witness: 9 independent points log in to add more points →

(-19, 6860)
(-498, 2549)
(269, 4083)
(74, 5601)
(67, -5700)
(534, 10178)
(272, 4100)
(363, 5363)
(-192, -8364)

Commentary

BASE records/rank_9.md#15 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:36 UTC · history

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