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curve #4534

y² + xy + y = x³ + x² − 177267159x + 4919066961780

a-invariants: [1, 1, 1, -177267159, 4919066961780]
c-invariants: [8508823633, -4250137671155321]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 2182440670557
discriminant (Δ): -10097008515794627143632259743
Faltings height: 4.0548
naive height: 71.9715
primes of bad reduction: 3, 7, 43, 109, 131, 193, 877
regulator: 2341.59754499349322031549281230492000516273076493
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:34:20 UTC
last updated: 2026-10-17 10:34:20 UTC

Witness: 5 independent points log in to add more points →

(21740, -3378480)
(1395/4, 17630005/8)
(1401159/1156, 85239468047/39304)
(-7500, 2417619)
(4711437/16, -10226543901/64)

Commentary

BASE torsion/torsion_Z4.tsv.gz:2420 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:34:20 UTC · history

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