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curve #4524

y² = x³ − 631437849x + 6127703285481

a-invariants: [0, 0, 0, -631437849, 6127703285481]
c-invariants: [30309016752, -5294335638655584]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 91008239663484
discriminant (Δ): -108229684108437832536840816
Faltings height: 3.8537
naive height: 72.4108
primes of bad reduction: 2, 3, 11, 13, 31, 41, 515149
regulator: 959.00110866486775976428532868263427106313508514616
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:48 UTC
last updated: 2026-10-17 10:33:48 UTC

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

(-4616, 2990663)
(14449, 143623)
(15720, 293601)
(15105, 190281)
(15339, 226083)
(16704, 490893)

Commentary

BASE torsion/torsion_Z3.tsv.gz:540 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:48 UTC · history

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