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curve #1672

y² + xy = x³ − 21976692209816x + 39311761957618920000

a-invariants: [1, 0, 0, -21976692209816, 39311761957618920000]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 5421733986630
discriminant (Δ): 11689165972778630239079567101479459225600
Faltings height: 6.5069
naive height: 103.7766
primes of bad reduction: 2, 3, 5, 13, 31, 37, 107, 227, 499
regulator: 698.674118993236292069111908639220145392655045969
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:56:19 UTC
last updated: 2026-09-25 02:56:19 UTC

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

(1741888, 2512297816)
(298949808/121, -414332988744/1331)
(1591600, 2891519080)
(2934768, 301891176)
(13792048, 48570255976)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:56:19 UTC · history

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