curve #388

y² + xy = x³ − 22712780660696177254170711756480x + 41395746156416669814359661263389227736207101952

a-invariants: [1, 0, 0, -22712780660696177254170711756480, 41395746156416669814359661263389227736207101952]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 41685244993537487215238075916551303005312462761232226482899426955171670
naive height: 228.2150
Faltings height: 16.8642
discriminant (Δ): 9599917880856536381058881627733998505888507258688104953135739473953992158955863999360000000000
primes of bad reduction: 2, 5, 7, 11, 13, 41, 53, 5417, 353777101065609033766265404563125673613664117715262750874987
regulator: 47162479584129012139227.18774671908581360386212870338744488452543994070844821
submitted by: y011d4
submitted at: 2026-08-27 04:15:59 UTC
last updated: 2026-08-27 04:15:59 UTC

(109886039440562132915153281/536756224, -1151587972032324017473810733172565364479/12435568197632)
(4765359035580765361363416/1543154089, -1610062580488842637174914711098171264/60619722078187)
(72379124907592152102336/24137569, -1880494597007422009939702239688384/118587876497)
(335020994863081278656/85849, -2777298628955145980239841671104/25153757)
(3526045176114994, 71754831169690059535378)
(2952688302920064, 8637603481704724752448)
(191549356675557343684/62001, 412423329387479878711750846352/15438249)
(730528075218445339056/237169, -2966487217010425208102027461696/115501303)
(892881267545452992/169, -576572178084322599155139008/2197)
(112915117962958054276/31329, 441999948837164674946485943824/5545233)
(4210398820124744, -142847999827071134844872)
(3311735603484744, 49987887295631234400128)
(445839058631301824/121, 117035331120286490577759168/1331)
(60725988327791904, -14919720768403365970956992)
(71201997226791800988008/21743569, 4684018653404243480127655351147560/101390262247)
(4762822888798736174351744/1242633001, 4520190626880924089474324523706216128/43804055918251)
(351083772062499188850944/74839801, 126348109143274448905124390584801728/647439118451)
(331812498152209744348354/55935441, -142117567427296709216577942508456658/418341163239)
(21984767255580196/9, 597700053401034166985956/27)

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