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curve #4361

y² + y = x³ − x² − 54763641088750x + 172268690794093723258

a-invariants: [0, -1, 1, -54763641088750, 172268690794093723258]
c-invariants: [2628654772260016, -148840133074168343335064]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 737638357126715
discriminant (Δ): -2308934233329494531315410880610882662196875
Faltings height: 6.8626
naive height: 106.7143
primes of bad reduction: 5, 11, 31, 41, 107, 191, 516319
regulator: 5023.29724871233846043477601281853686926185899731
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:19 UTC
last updated: 2026-10-17 10:06:19 UTC

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

(19888547, 83367255966)
(26443121381/3364, 2942861203494479/195112)
(2912807911/729, 81735317265446/19683)
(3220003654/81, 179780283870598/729)
(212862316/49, 1386856907666/343)

Commentary

BASE torsion/torsion_Z5.tsv.gz:1298 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:19 UTC · history

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