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curve #4495

y² + xy = x³ − x² − 3499x + 137089

a-invariants: [1, -1, 0, -3499, 137089]
c-invariants: [167961, -117689085]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 2636686970374
discriminant (Δ): -5273373940748
Faltings height: 1.1357
naive height: 37.1671
primes of bad reduction: 2, 1318343485187
regulator: 989.5736835097047111588122902549742562999163232562097
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:28 UTC
last updated: 2026-10-17 10:31:28 UTC

Witness: 7 independent points log in to add more points →

(-14, 435)
(1, 365)
(32, 223)
(39, 223)
(58, 327)
(64, 383)
(100, 833)

Commentary

BASE records/rank_7.md#17 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:28 UTC · history

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