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curve #4500

y² = x³ − x² − 4053735065x + 475577092790361

a-invariants: [0, -1, 0, -4053735065, 475577092790361]
c-invariants: [194579283136, -410897440695173120]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 168526126573084140864
discriminant (Δ): -93443125910882248801930715394048
Faltings height: 4.8163
naive height: 81.1142
primes of bad reduction: 2, 3, 23, 41, 73, 79, 223, 503, 857
regulator: 553346.75785600136379553113282880750428901284278325038940
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:35 UTC
last updated: 2026-10-17 10:32:35 UTC

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

(89501, 28804464)
(35089, 19404568)
(197879, 86148468)
(68985, 22895856)
(-107453/9, 617039216/27)
(25745, 19704744)
(-29443, 23862240)
(-6155/4, 175601573/8)
(51368, -20072007)

Commentary

BASE torsion/torsion_Z2.tsv.gz:644934 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:35 UTC · history

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