curve #1085

y² = x³ − 43957892034985974408867x + 3504959683923441655614250399616674

a-invariants: [0, 0, 0, -43957892034985974408867, 3504959683923441655614250399616674]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 81988082219777126188462072560
discriminant (Δ): 129130227595112861668085662911581546138422360781345097730457856000000
Faltings height: 11.8751
naive height: 168.0262
primes of bad reduction: 2, 3, 5, 7, 11, 31, 41, 89, 107, 109, 127, 131, 137, 163, 337, 1279
regulator: 34793650.04158184820278489363428946905380955456789325350620
submitted by: dujella
submitted at: 2026-09-23 17:45:49 UTC
last updated: 2026-09-23 17:45:49 UTC

(107768287313, 4394796747081840)
(94555380033, 13924714157729600)
(31812992183, 46246345487877150)
(41570646023, 41826316133193570)
(-11735013087, 63397082640559360)
(-116884679742, 83940943569093050)
(109609638033, 1905554145664400)
(-90570410497, 82117568157173010)
(136668620753, 7073495137391760)
(134998901009, 5568436197379440)

Dujella - Peral (2023), induced by the rational Diophantine triple {-18265737/79309750, 63575946/991371875, -310970944/991371875}

last edited by dujella at 2026-09-23 17:45:49 UTC · history