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curve #4506

y² = x³ − x² − 279749385x + 1518333495561

a-invariants: [0, -1, 0, -279749385, 1518333495561]
c-invariants: [13427970496, -1311759572341760]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 106037595064676544
discriminant (Δ): 405375835331777394800627712
Faltings height: 3.8267
naive height: 69.9618
primes of bad reduction: 2, 3, 23, 71, 73, 89, 137, 409, 929
regulator: 25530.6054079212545971406792047435521688545701807063322
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:52 UTC
last updated: 2026-10-17 10:32:52 UTC

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

(-6267, 1739352)
(-5856, 1719213)
(2243, 949808)
(-18049, 829124)
(1887, 998580)
(3489, 764688)
(25791, 3384996)
(2192709/169, 592287168/2197)

Commentary

BASE torsion/torsion_Z2.tsv.gz:635300 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:52 UTC · history

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