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curve #4248

y² = x³ − x² − 75459410575x + 21007795589220391

a-invariants: [0, -1, 0, -75459410575, 21007795589220391]
c-invariants: [3622051707616, -18150713656776172160]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 168010591633224367516032
discriminant (Δ): -163153804013067166330169176358899968
Faltings height: 5.4428
naive height: 88.6905
primes of bad reduction: 2, 3, 23, 41, 73, 127, 223, 911, 1481, 4057
regulator: 13350614.50369941357026185672255081052834061612906939090614
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:12:09 UTC
last updated: 2026-10-15 18:12:09 UTC

Witness: 10 independent points log in to add more points →

(227559, 124979942)
(728215, 593487054)
(-337826, 89134533)
(7419373, -20195940852)
(37789861/196, -320309671779/2744)
(1581271, 1963548306)
(47638462/169, 326866676319/2197)
(-2610, 145618429)
(2629303, 4242591522)
(100164334/25, 1000271042577/125)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-15 18:12:09 UTC · history

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