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curve #4461

y² + xy + y = x³ − x² − 31x + 6

a-invariants: [1, -1, 1, -31, 6]
c-invariants: [1473, 1215]
rank (lower bound): ≥ 4
torsion subgroup: trivial
conductor (N): 1848689
discriminant (Δ): 1848689
Faltings height: -0.1080
naive height: 21.8852
primes of bad reduction: 191, 9679
regulator: 10.48075399525355228684810192165702824857912873
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:59 UTC
last updated: 2026-10-17 10:24:59 UTC

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

(-3, 9)
(-2, 8)
(0, 2)
(12, 29)

Commentary

BASE records/rank_4.md#16 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:59 UTC · history

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