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curve #4249

y² = x³ − x² − 699947400265x + 185534315352193561

a-invariants: [0, -1, 0, -699947400265, 185534315352193561]
c-invariants: [33597475212736, -160301446879443960320]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 351824891684388520040832
discriminant (Δ): 7076360890860375532399305678840471552
Faltings height: 5.7889
naive height: 93.4364
primes of bad reduction: 2, 3, 7, 73, 137, 257, 263, 337, 401, 673, 2129
regulator: 4868464.209315494553085860874768226247862341089478224481983
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:12:19 UTC
last updated: 2026-10-15 18:12:19 UTC

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(651589, -78101532)
(2669893, -4165167132)
(-7114223/9, -13361659244/27)
(-875936, -355764843)
(-866291/25, 57247684452/125)
(-910631, -260360532)
(37221, 399415996)
(-632043, -612734260)
(267609, 131858732)
(211399, 216825768)

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 18:12:19 UTC · history

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