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curve #1572

y² + xy + y = x³ + x² − 28224536135830x + 57714693438030318227

a-invariants: [1, 1, 1, -28224536135830, 57714693438030318227]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/8ℤ
conductor (N): 990867570
discriminant (Δ): 12270206888217894205821758353347628800
Faltings height: 6.3161
naive height: 104.5272
primes of bad reduction: 2, 3, 5, 7, 11, 31, 101, 137
regulator: 212.90216784812822686147841636381285598371862
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:16:18 UTC
last updated: 2026-09-25 01:16:18 UTC

Witness: 3 independent points log in to add more points →

(11089734257/3721, 59150085764451/226981)
(3072717, 3621871)
(267977291/100, 1149005427009/1000)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:16:19 UTC · history

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