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curve #4501

y² = x³ − x² − 11494969455x + 461669491755351

a-invariants: [0, -1, 0, -11494969455, 461669491755351]
c-invariants: [551758533856, -398879130325420160]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 584355605739340152192
discriminant (Δ): 5133921777489406839844341987072
Faltings height: 4.6687
naive height: 81.1091
primes of bad reduction: 2, 3, 23, 31, 41, 73, 367, 487, 4231
regulator: 961320.27087332411599838557829435747681588719008300010280
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:38 UTC
last updated: 2026-10-17 10:32:38 UTC

Witness: 9 independent points log in to add more points →

(23343, 14354838)
(-66939, 30515316)
(35454, 9934323)
(559829/4, 319432763/8)
(38390, 8772401)
(-81986, -29206227)
(-14459, 24997044)
(745599, -637481202)
(323549, -174965048)

Commentary

BASE torsion/torsion_Z2.tsv.gz:644942 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:38 UTC · history

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