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curve #4451

y² + y = x³ + x² − 112x + 20

a-invariants: [0, 1, 1, -112, 20]
c-invariants: [5392, -49816]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 89284469
discriminant (Δ): 89284469
Faltings height: 0.2154
naive height: 25.7780
primes of bad reduction: 43, 2076383
regulator: 30.6578925838195371475590581734743926633005281404
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:30 UTC
last updated: 2026-10-17 10:24:30 UTC

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

(-10, 15)
(-9, 19)
(-4, 20)
(-2, 15)
(-1, 11)

Commentary

BASE records/rank_5.md#15 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:31 UTC · history

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