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curve #4449

y² + xy = x³ − x² − 784x + 4684

a-invariants: [1, -1, 0, -784, 4684]
c-invariants: [37641, -3877605]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 11080913666
discriminant (Δ): 22161827332
Faltings height: 0.6823
naive height: 31.6075
primes of bad reduction: 2, 2927, 1892879
regulator: 1168.1827071542576074656795142396175781060257540171
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:25 UTC
last updated: 2026-10-17 10:24:25 UTC

Witness: 6 independent points log in to add more points →

(-30, 38)
(-28, 78)
(-25, 103)
(-21, 118)
(-14, 120)
(173, 2155)

Commentary

BASE records/rank_6.md#16 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:25 UTC · history

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