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curve #1363

y² = x³ − 214537904212725x + 1209909094426242384525

a-invariants: [0, 0, 0, -214537904212725, 1209909094426242384525]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 8016738491175953348700
discriminant (Δ): -432551470918127221449529127176342264470000
Faltings height: 6.9534
naive height: 110.6128
primes of bad reduction: 2, 3, 5, 11, 31, 41, 83, 179, 211, 7527307
regulator: 224311.233363448886449778634208956346676342916819281758
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:39:01 UTC
last updated: 2026-09-24 17:39:01 UTC

Witness: 8 independent points log in to add more points →

(-13812915, 39215372295)
(-6632585, 48384653705)
(1398495, -30209502945)
(-16015755, 23190167055)
(7338780, 5541873855)
(-13988045, -38391385645)
(4512445, 18267504695)
(1850220340/81, -66125213511445/729)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:39:01 UTC · history

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