curve #1987

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y² = x³ − 6691138199936854275485513914527733997247x + 210914104354792111895456282950934164254494025766186699421250

a-invariants

[0, 0, 0, -6691138199936854275485513914527733997247, 210914104354792111895456282950934164254494025766186699421250]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

2435407810164844062203703218408468634622745221920921014678247525496384669262556650704884919101576

discriminant (Δ)

-44861880564479636734789627921135943648533186298668158238340415451303729178051724143292442077114337304772200798083753728

Faltings height

21.6725

naive height

286.7207

primes of bad reduction

2, 3, 7, 11, 13, 23, 31, 103, 179, 51586514219, 49829800921377844475545989393622603116689832643393261118584612050915981647

regulator

303199619089093115452986018.6908999871940616386112848082867749174340508268753316215664149

submitted by

Ritik Jain

submitted at

2026-09-25 23:06:13 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:17:14 UTC

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

(9170668146161340606969/64, -758428664747220782474806909603341/512)
(4313972181025123708014069/1849, -8954730941332905851836359159570202146/79507)
(-177442508029590577575/4, 5187316561893899044063598351205/8)
(611675872061050935009, 14999167531588420165733857160766)
(-367487037229058808863/4, 1792508737136405690312740252423/8)
(-38674396531538411799, -641750882688433754724462354198)
(5544537129808217277498, 412810698982921821183348229646394)
(1016148708098455137699/25, -9760681838249759454168796833168/125)
(-624325130108831609663/16, -41109362219659765998053344594337/64)
(156031638681782108943492261/2449225, -796675237843071890374824531620299091634/3833037125)
(47031361009168080075, -15866197567344727672901471640)
(3219211572162435241109721/52900, 2075163842501464158779938221385890981/12167000)
(280991732998883087788729/5625, 15329641222124261237380171139855558/421875)
(13590058064376043953, -349987272842057760916933471506)
(49097762946644269339, -27363837018825918221098707856)
(496136106656810370833325/10201, 23729473795446468676263701612137590/1030301)
(40467489434988989211, 80067577467302016937223254992)
(-208758199947239100810330827615631/17239818151396, 38558427255961353592956578603295876025224457096689/71581207588957212056)
(-111120513384738393565513006238848250017907837096585210159007708898002837111/1200071303937715022263178796307793065052820941718624004, 251463949585750953176101287152709402245241694954993347215504977312679612342517862409400092808562309292838316179/1314651304078232352527101675296338590525923425725731151008305400661738135757622008)
(1554434297647046440480300816734150496936666831659318114559652943433/13384357561836620842317686125113721782093972496, 1548676440227929906061885990528108700823999454427310750922207834629006219078698949069140371368033211/1548446823095552559231661001452971001242487335561383296531754684868544)
(55821791734023077945520146724441392109/1266574932429384769, 57447444027412787410530578451050140025240591478217410726/1425431436727510430017996897)
(460179831707816108982133018030247396794280061966931/23259063347479268015733715525929, 32948109260138894867865847819092965525573644693603282829464835480721114219248/112172999302962598926399958237759771058848389717)
(1110428736833383995123980520286200158946577149249628713810804253094029/23965771681018502870951842553279694596451374443041, 2221688213751353982060330144503429359657419629436737802647072770137936810280001187048120629593080164806/117324071606392416202670684978303315474553389383377073145736873281872213839)
(9707723027911470967644732432695513520401871934573/158902316313892251293426547601, 10998715754828847059821443432827877687564615403923140382308089082496140006/63342520685913106770300631215387402246518599)
(-90059075806957304613005635778002842103347903/1094902606381534066426489, 518465812216933309263142209222446470817472715869885081395542874622/1145679743213109227240452100905368013)

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