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curve #4462

y² + y = x³ + x² − 534x + 4578

a-invariants: [0, 1, 1, -534, 4578]
c-invariants: [25648, -4109464]
rank (lower bound): ≥ 4
torsion subgroup: trivial
conductor (N): 709111
discriminant (Δ): -9218443
Faltings height: 0.2848
naive height: 30.4576
primes of bad reduction: 13, 54547
regulator: 21.51032725719663105083540784323457996391382781
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:25:01 UTC
last updated: 2026-10-17 10:25:01 UTC

Witness: 4 independent points log in to add more points →

(-27, 6)
(-14, 97)
(24, 78)
(38, 201)

Commentary

BASE records/rank_4.md#6 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:25:02 UTC · history

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