curve #3843

y² + xy = x³ − 1390269098748159733410018666x + 18994312040136079780696595045235498849700

a-invariants: [1, 0, 0, -1390269098748159733410018666, 18994312040136079780696595045235498849700]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 31566406933966762584842830
discriminant (Δ): 16120820632542003947724008010513726964798268655270722339665926962139147809482342400
Faltings height: 14.5301
naive height: 199.1115
primes of bad reduction: 2, 5, 11, 13, 19, 37, 61, 73, 181, 223, 307, 317, 787, 2281
regulator: 37395147.3286779265654524198687290232171993386782374515
submitted by: dujella
submitted at: 2026-10-03 17:24:26 UTC
last updated: 2026-10-03 17:24:26 UTC

(5262666920508, 108736108636602196966)
(28928316270708, 54632910473699965766)
(-921621848436, -142389716876102534194)
(16900639679386, 18034183021528197484)
(28984464572276, 55208062009768919110)
(-42764964681442, -15451472883290455224)
(14172298157300, 46233823868631052870)
(13889466896874, 48618237964480256860)

the same construction as #3834, with parameters v = −3/22 and w = 680/1601

last edited by dujella at 2026-10-03 17:24:26 UTC · history