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curve #4432

y² + y = x³ − 216517x + 38753856

a-invariants: [0, 0, 1, -216517, 38753856]
c-invariants: [10392816, -33483331800]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 810785363339557
discriminant (Δ): 810785363339557
Faltings height: 1.7957
naive height: 48.4699
primes of bad reduction: 263, 401, 7687865539
regulator: 10959.9356104070565644266631890009127137663012379642050
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:41 UTC
last updated: 2026-10-17 10:23:41 UTC

Witness: 8 independent points log in to add more points →

(275, 92)
(262, -106)
(277, 180)
(342, 2169)
(309, -1164)
(1097/4, 279/8)
(246, 614)
(177, -2445)

Commentary

BASE records/rank_8.md#37 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:41 UTC · history

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