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curve #1369

y² = x³ − x² − 27370426505x + 800448048863241

a-invariants: [0, -1, 0, -27370426505, 800448048863241]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1752168876938623852224
discriminant (Δ): 1035490968344555729018679297871872
Faltings height: 5.0300
naive height: 83.7118
primes of bad reduction: 2, 3, 31, 73, 79, 97, 257, 857, 1249, 1913
regulator: 903766.19922856796766131403266526014981882140651739377950
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:40:05 UTC
last updated: 2026-09-24 17:40:05 UTC

Witness: 9 independent points log in to add more points →

(-177355, 8719704)
(-132679, 45785016)
(237869, 88027488)
(-13825, 34295796)
(24569, -11950488)
(387811, 220253264)
(29965, -2682896)
(206585, 62949096)
(-5293, 30743640)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:40:05 UTC · history

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