curve #1881

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y² + xy = x³ − 1115370772374667084087516921954512890550x + 14375882358703204420880299553233452255473713820659414702500

a-invariants

[1, 0, 0, -1115370772374667084087516921954512890550, 14375882358703204420880299553233452255473713820659414702500]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

3878678960948734387609005621563626933099032185816747167253931173213742798446087251239976685519190

discriminant (Δ)

-474640728914413204833691103946374176942155663421021189566406474312830277006399832774149442590520378933834674406400000

Faltings height

21.2562

naive height

281.3490

primes of bad reduction

2, 3, 5, 11, 13, 19, 41, 43, 1052798544353, 1920113472454111536047087650350387443, 310513154169956385418792075395673435379

regulator

339938298845655930899984327.6051713960427675603975350479004436617782056578392116532563196

submitted by

Ritik Jain

submitted at

2026-09-25 17:33:51 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:42:16 UTC

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

(-7335619124128466868, 148872691480149439876983988602)
(2172923587642492397153646131676648101113039441020/13439150073324993145396939441, 3139559241135064375336404470599076734348493708321380686713995985514797850/1557965030795117913276796177071306891462761)
(138424353135197938020/49, -36376633070354244122693311692690/343)
(287865425899811915518950/19321, 87652172695865850729773229511093050/2685619)
(32003882136529444618830/1849, -1271578800541876902024120976688550/79507)
(40667994720283730876715/5476, -32675457684662373359968521647752485/405224)
(315484161615774313440, -5573393357135052234903400653990)
(19049213631441751538952/841, -660297202406555300153224332089886/24389)
(19368383423590125072, 6220778186631162474303631002)
(35845492140967279932, -143012992812721361064985164534)
(22258034330326444356, -24020800109771161503340072158)
(13982407985258305182, 38909922281966567302152367716)
(332135603725671848325/16, -828570172353511991428930827225/64)
(17453486982890291910, -15017581323870803763859338210)
(6979622716039444924932/841, -1839846377902153557846139908794622/24389)
(645929485158588047244/49, 15198799701844608652446463720566/343)
(-382701290182825302830571897925620/18150096445849, -13058378507616917820538575199923528299332841357550/77324728837575373757)
(-16487786673711657000, 168177645871459750424543021550)
(8293813625935717405623/484, 182808404059077758286725145352623/10648)
(-12108469820573918644, 161573611374895822133473947002)
(1443349140334518091953447750/314104729, 538223718526664603860613401314623405804100/5566878112067)
(-404486306595771265455996660810816832159031820/10515152838261438404081521, 647733877040484790094204286325095227919609625588593599629834279170/34097566443987959669612359231761260681)
(6819376162271822184364218458676704756544300/532164854603954344524361, 18156177450509310914424494343398681454002019922751770383290004450/388212293477841236669880165867059141)
(411373643732212268074272148309416378765330/92306755781707855916641, 2732540828570285349481832553150270569425340189687160485089051650/28044663360946668614420459630515439)
(1099736065816374320920344390701640966/55545446559064225, 96077025118130443535455363396386981811833989690905794/13090996114579202185343375)

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