curve #1889

y² + xy = x³ − 281907682665212636885865424946239989566788x + 57883150559257556608902424131863735984606700809995228366514192

a-invariants: [1, 0, 0, -281907682665212636885865424946239989566788, 57883150559257556608902424131863735984606700809995228366514192]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 27330508052550357100235030734447882965057646891476747278273138253658120297429452622727157827826450
discriminant (Δ): -13558283068684659736623245538187132875301598652658406213740731479893673310696136930362791752910872949502783883245848064000000
Faltings height: 22.6624
naive height: 297.9502
primes of bad reduction: 2, 3, 5, 13, 17, 31, 37, 41, 43, 71, 379, 25111, 256163, 2355431477228204998525436412292127519369747595959581001965149190033145719
regulator: 248915041952252528897308478.4198511644422853984384257817730924622299248598672867846526849
submitted by: Ritik Jain
submitted at: 2026-09-25 17:34:30 UTC
last updated: 2026-09-25 17:34:30 UTC

Witness: 25 independent points log in to add more points →

(284689793953725094291458552848/772450849, -43185681518736462444401067708717516928177732/21468726446257)
(24492294166796287320282215682693018941665006144442168/880464870152674434771640634777761, -184852476949997016755257868351165350688951292470910417321905585994815636741058548/26125706822101426624659127119719186999393161072241)
(5519468524296727531653272/19321, 2187222598152190440205315824399280196/2685619)
(71241652646163572728472/121, -13041394126791785014602501193198796/1331)
(-332136849749154423118, 10717996135825376888850995508134)
(715572380091845090457911/100, -603692846245458377072696558849284639/1000)
(3118562457948657387450092/2809, -4967435868515881941356501446471546520/148877)
(-263540876862795575498804/441, -33306297897109546634373572390106820/9261)
(91480731565145541032, -5732329939228851063394297034116)
(1532029591295235023950523/3364, -954930998662650621185602342858021717/195112)
(3476118581095133624765108/12769, 1654052356310162241450200023469794348/1442897)
(155793084139022118203848/1089, 162636966834218872534854143887253308/35937)
(135987855146937767522, 4697010922927839917608124017064)
(72040743643247635124926/225, 2252173678935810584464604193713206/3375)
(215356453226141334006152/361, -69276120127534988490985706914947244/6859)
(204566473503759344323469624/994009, -2903390858098008044699286628051197169060/991026973)
(6252344806086100452480645743139055172/3345256106799721, -15061799368414815015160614812570409009835982127235696804/193483554958486448345269)
(23957151932259678607915745896/76895361, 366213594202039041847027130716790037617020/674295420609)
(169885234764175815272, 3859307486710565981605583739164)
(1279590236095559894068874/4489, 249228893293783646362600879848503402/300763)
(286416524999262954632, 797588167731725681947070047484)
(6013922916315398590458892944577286503808519966943833360402/17713049558612984430612049405446625009, 85246121319675985168338008763440325921342896474499506324287020919633801952332804102376/74548688340753826222291008374557331110192689142287062473)
(1741081022575440117289797639841213424372237785718/5552374724385511777973763169, 233140913908815364842852078887825922745073497766335839220578326942090642/413731085672391620182169070512224745025553)
(209847960846204446774919608539849999912808363/550660342677727967282404, 983728122740255297674991931708464472974717796076862069085636372037/408625722091167459420852059765677208)
(-4159455887110323816454171608862237303954421632/11653078374911083665352249, 422921278995188312456642263008473779233671421611028393268780988367412/39779653975942075845721098862734899693)

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