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curve #4454

y² + y = x³ − 37x + 636

a-invariants: [0, 0, 1, -37, 636]
c-invariants: [1776, -549720]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 171637883
discriminant (Δ): -171637883
Faltings height: 0.2605
naive height: 26.4343
primes of bad reduction: 449, 382267
regulator: 33.1482500980862688359881611675968816359560169658
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:38 UTC
last updated: 2026-10-17 10:24:38 UTC

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

(-8, 20)
(-2, 26)
(3, 23)
(4, 23)
(14, 53)

Commentary

BASE records/rank_5.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:38 UTC · history

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