curve #1228

y² + xy = x³ − x² − 1053711230239x + 573871088239158649

a-invariants: [1, -1, 0, -1053711230239, 573871088239158649]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 33696601705258235525930879596769745214
discriminant (Δ): -67393203410516471051861759193539490428
Faltings height: 5.9630
naive height: 95.3055
primes of bad reduction: 2, 105907, 31206899, 5097776928898745253724999
regulator: 651471396475.56750017292713503535460265462073008114524843528658913036
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:36:00 UTC
last updated: 2026-09-24 14:36:00 UTC

(230856, 585477299)
(302220, 531847253)
(653186, 404993559)
(1139236, -923614395)
(-805619, 949031270)
(-964879, 832516150)
(-1217484, 228884519)
(698995, 422564927)
(887066, 580227619)
(476964, 423784343)
(208421, 602647125)
(-240254, 901874775)
(-12689756/25, 123645594993/125)
(1426125, 1403439718)
(805140, 497008613)

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

last edited by Michael Rubinstein at 2026-09-24 14:36:00 UTC · history