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curve #4509

y² = x³ + x² − 429865120x + 3101118161604

a-invariants: [0, 1, 0, -429865120, 3101118161604]
c-invariants: [20633525776, -2679489892780480]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 92683481879444048
discriminant (Δ): 928761810705278116664148992
Faltings height: 3.9093
naive height: 71.2505
primes of bad reduction: 2, 37, 41, 47, 61, 73, 173, 263, 401
regulator: 39372.6858298368488221784336235304774208926107638767231
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:00 UTC
last updated: 2026-10-17 10:33:00 UTC

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

(5992, 860546)
(27526, 3482144)
(-5626, 2311168)
(-22298, 1264976)
(-2576, 2047282)
(-9246, 2507052)
(2187889/16, 3200800847/64)
(7550, 534848)

Commentary

BASE torsion/torsion_Z2.tsv.gz:635298 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:00 UTC · history

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