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curve #4498

y² + y = x³ + x² − 270x + 8850

a-invariants: [0, 1, 1, -270, 8850]
c-invariants: [12976, -7724440]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 33265115083
discriminant (Δ): -33265115083
Faltings height: 0.7004
naive height: 31.7198
primes of bad reduction: 137, 3413, 71143
regulator: 279.23221272974514850285958251331558844425843807012
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:35 UTC
last updated: 2026-10-17 10:31:35 UTC

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

(-25, 24)
(-23, 58)
(-21, 75)
(6, 86)
(12, 86)
(24, 129)

Commentary

BASE records/rank_6.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:36 UTC · history

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