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curve #1722

y² = x³ − x² − 50209160669889x + 136913510861910900129

a-invariants: [0, -1, 0, -50209160669889, 136913510861910900129]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 666025540226112
discriminant (Δ): 2845984335349021847898872944595482804224
Faltings height: 6.5682
naive height: 106.2553
primes of bad reduction: 2, 3, 11, 23, 73, 311, 8273
regulator: 40176.612729233761832897280647910725256403716256581
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:15:57 UTC
last updated: 2026-09-25 06:15:57 UTC

Witness: 6 independent points log in to add more points →

(1910624, 6925126879)
(37255480/9, 1891576511/27)
(41666029/9, 51877275560/27)
(-1502875, 14456042248)
(16163053/4, 660023295/8)
(4039285, 92980392)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:15:58 UTC · history

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