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curve #1360

y² + xy = x³ − x² − 133531298828661309x + 18781146648346242171304565

a-invariants: [1, -1, 0, -133531298828661309, 18781146648346242171304565]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 476332283040496536245130
discriminant (Δ): 435446297061877384450523329023413513963678250000
Faltings height: 8.4038
naive height: 129.9129
primes of bad reduction: 2, 3, 5, 7, 11, 71, 397, 503, 733, 104982139
regulator: 921791.112961269549858941685390268236293916129379629568
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:38:30 UTC
last updated: 2026-09-24 17:38:30 UTC

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

(211229510, 3661749615)
(1861292374/9, 2813349458389/27)
(231657346, 528619421887)
(216657886, 143409718507)
(208750726, -55722478673)
(-179756414, 6080870962207)
(5654724286/25, -48425687432149/125)
(210493621, 10835195587)

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 17:38:30 UTC · history

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