curve #3447

y² + xy = x³ − 829248587546232242x + 341761829044265374567063684

a-invariants: [1, 0, 0, -829248587546232242, 341761829044265374567063684]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 762619546977047970820027222
discriminant (Δ): -13963026339178552572139643957882399364443836924337629696
Faltings height: 9.3018
naive height: 135.7155
primes of bad reduction: 2, 7, 23, 43, 89, 311, 2383, 22639, 74821, 492979
regulator: 13899215.606402574980722878068523895714005336538444126405
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:35:11 UTC
last updated: 2026-09-27 05:35:11 UTC

(-189916826, -22189995004600)
(832446100, -15110490503778)
(-195069021338/361, 172444749469472198/6859)
(133172679624/25, 47938500341854022/125)
(5694975884, 424641641525726)
(504268770228/121, 350300094688740170/1331)
(15040050644, -1841196335033074)
(2200557492, 95774937817822)
(5965919830, 455776283293592)

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

last edited by Michael Rubinstein at 2026-09-27 05:35:11 UTC · history