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curve #4520

y² = x³ − x² − 535049x + 138777609

a-invariants: [0, -1, 0, -535049, 138777609]
c-invariants: [25682368, -119749760000]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 276672153792
discriminant (Δ): 1504441356968300544
Faltings height: 2.2279
naive height: 51.1839
primes of bad reduction: 2, 3, 17, 41, 73, 127, 223
regulator: 553.26501439887388492076403185045682564275597196510
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:29 UTC
last updated: 2026-10-17 10:33:29 UTC

Witness: 6 independent points log in to add more points →

(575, -4572)
(-187, -15240)
(67, -10160)
(-695, 13208)
(829, 16256)
(4385, 286512)

Commentary

BASE torsion/torsion_Z2.tsv.gz:8252 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:29 UTC · history

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