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curve #4511

y² = x³ + x² − 35263769x + 80522169511

a-invariants: [0, 1, 0, -35263769, 80522169511]
c-invariants: [1692660928, -69581310423040]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 354523152688576
discriminant (Δ): 4679274515335533891584
Faltings height: 3.0792
naive height: 63.7487
primes of bad reduction: 2, 17, 41, 89, 271, 433, 761
regulator: 12927.63833744593247645744287720202559696665914051392
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:05 UTC
last updated: 2026-10-17 10:33:05 UTC

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

(1825, 149156)
(5515, 231976)
(-2741, 395720)
(6391, 340928)
(-5325, 342544)
(22859, 3349560)
(30743, 5296560)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315568 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:05 UTC · history

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