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curve #4507

y² = x³ + x² − 433739145x + 1718202086839

a-invariants: [0, 1, 0, -433739145, 1718202086839]
c-invariants: [20819478976, -1484651519902720]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 184144131532505536
discriminant (Δ): 3946775289835044013352456192
Faltings height: 3.9912
naive height: 71.2775
primes of bad reduction: 2, 7, 17, 79, 281, 569, 727, 2633
regulator: 38797.9451632492578684132534101969394849941261204476905
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:55 UTC
last updated: 2026-10-17 10:32:55 UTC

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

(-5278, 1964809)
(118989, 40432832)
(-336063/16, -80004169/64)
(-1693, 1564504)
(-16233, -2117024)
(-6621, -2073592)
(3570, -463967)
(24479, -2402008)

Commentary

BASE torsion/torsion_Z2.tsv.gz:635320 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:55 UTC · history

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