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curve #4523

y² = x³ − 678295692x + 6796972907649

a-invariants: [0, 0, 0, -678295692, 6796972907649]
c-invariants: [32558193216, -5872584592208736]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 42333714289620
discriminant (Δ): 14817903086726873199378000
Faltings height: 3.7900
naive height: 72.6189
primes of bad reduction: 2, 3, 5, 13, 37, 41, 59, 607
regulator: 883.83029675899873694900247944330387505603450728917
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:46 UTC
last updated: 2026-10-17 10:33:46 UTC

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

(13230, 372567)
(24423, 2190630)
(27088, 2880865)
(6834, 1575015)
(128131/9, 4338620/27)
(529026/25, 173170101/125)

Commentary

BASE torsion/torsion_Z3.tsv.gz:504 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:46 UTC · history

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