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curve #4532

y² = x³ − x² − 5245x + 3502381

a-invariants: [0, -1, 0, -5245, 3502381]
c-invariants: [251776, -3024546560]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 17665523904
discriminant (Δ): -5284676806929408
Faltings height: 1.6961
naive height: 43.6601
primes of bad reduction: 2, 3, 7, 19, 37, 2671
regulator: 552.669673265800950512217545674068546848849818689
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:34:15 UTC
last updated: 2026-10-17 10:34:15 UTC

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

(-135, 1316)
(-19, 1896)
(-156, 707)
(89, 1932)
(-99, 1744)

Commentary

BASE torsion/torsion_Z2.tsv.gz:458 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:34:15 UTC · history

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