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curve #4052

y² + xy = x³ − x² − 47557880628831x + 126237393066908251773

a-invariants: [1, -1, 0, -47557880628831, 126237393066908251773]
c-invariants: [2282778270183897, -109069097337306513704349]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 7604705611780974
discriminant (Δ): -194153279625442572994740271617441284976
Faltings height: 6.4788
naive height: 106.0925
primes of bad reduction: 2, 3, 19, 71, 109, 163, 199, 283, 313
regulator: 15963.25592733297905136626086743789022025645139207122
submitted by: Michael Rubinstein
submitted at: 2026-10-07 22:24:54 UTC
last updated: 2026-10-07 22:24:54 UTC

Witness: 7 independent points log in to add more points →

(4129722, -519101487)
(3828834, 524148849)
(177492522/49, 419033047539/343)
(364232331/49, -4646944332099/343)
(24929585058/6241, 29349477157251/493039)
(9360940386/2209, -93197958567069/103823)
(669266211/169, -191169194046/2197)

Commentary

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

last edited by Michael Rubinstein at 2026-10-07 22:24:54 UTC · history

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