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curve #4429

y² + y = x³ − 121849x + 38046702

a-invariants: [0, 0, 1, -121849, 38046702]
c-invariants: [5848752, -32872350744]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 509558981564991851
discriminant (Δ): -509558981564991851
Faltings height: 2.0855
naive height: 48.4318
primes of bad reduction: 509558981564991851
regulator: 1155040.6984117498672222837696190122046597607066463896441
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:33 UTC
last updated: 2026-10-17 10:23:33 UTC

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

(-453, 533)
(-452, 881)
(-451, 1125)
(-410, 4368)
(-400, 4773)
(-391, 5090)
(-332, 6473)
(-303, 6866)
(-190, 7371)

Commentary

BASE records/rank_9.md#14 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:33 UTC · history

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