curve #440

y² + xy = x³ − 251999675509943915172708010850520040x + 56079773175596610092961984688743586678074315954876992

a-invariants: [1, 0, 0, -251999675509943915172708010850520040, 56079773175596610092961984688743586678074315954876992]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 586774895615009250149605997681881087442462943383557157519246543306555254817070
discriminant (Δ): -334425938899067339777834986493481820088030699836403336760043084734488063375378621720519095470050816409600000
Faltings height: 19.3561
naive height: 256.4404
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 47, 53, 71, 73, 103, 401, 2748979313198597, 100220495663326957006673313156700481105233891
regulator: 80966098031179752453.2230627766397803113949009599079042636925778906634131434877
submitted by: Nikita-Shulga
submitted at: 2026-08-30 13:39:03 UTC
last updated: 2026-08-30 13:39:03 UTC

(246148664778310984, -94680154492468941934283552)
(-78436117248708376, 274523391882549488854253888)
(210456413323232469058/9, -3052418691515275972002880779010/27)
(8982271102497454948/169, 454711327001705594191390587976/2197)
(6779889361040488666/9, 14633582113463922288429519926/27)
(160126136700301274, 140832288916722173275308338)
(128284653222603224, 160820572635374504452324688)
(-223480165296527296, 318175025119443173147686568)
(2444791465340090864, -3748669723264524592539594472)
(6256785713510245624, 15601796729262529704541238488)
(-565333563800208976, -133648375931934013790899912)
(441857756201541104, 176066205694361191916359928)
(1007687629732598504, 908506168960262175834705368)
(1454226854291124671/4, 895005045572403826348867129/8)
(530118220590209024, -267332752317605254682043112)
(367036527786856274, 114159149319945194769929588)
(362124696337772624, 110956902323229524142596888)
(1585279574507599814, 1908028797127065643739839478)
(554729991376762352, 294944881863465806163988760)
(508127533420697264, 243366126763518796344271928)

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