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curve #4505

y² = x³ − x² − 575827145x + 5275024540041

a-invariants: [0, -1, 0, -575827145, 5275024540041]
c-invariants: [27639702976, -4557455364377600]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 143073212630034624
discriminant (Δ): 199675695082101992952532992
Faltings height: 3.8673
naive height: 72.1276
primes of bad reduction: 2, 3, 7, 19, 31, 41, 43, 1033, 99241
regulator: 14770.3888493747452432880540532229155366274906296398026
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:32:50 UTC
last updated: 2026-10-17 10:32:50 UTC

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

(-19447, 3019632)
(-17851, 3140928)
(5519, 1505028)
(16169, 437472)
(39016, -6496081)
(15301, 215264)
(-2927, 2633512)
(15469, 262472)

Commentary

BASE torsion/torsion_Z2.tsv.gz:635306 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:32:50 UTC · history

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