curve #1988

y² + xy = x³ − 37028665640007446366796577550396536028853015x + 99404505709503147313487857180814132828975074564769186811371253225

a-invariants: [1, 0, 0, -37028665640007446366796577550396536028853015, 99404505709503147313487857180814132828975074564769186811371253225]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 2214903586974390611924528749939108107618037383140024953022412792850465553855579948986664573718930
discriminant (Δ): -1019369941168087922653287978665026164317485602787065754513229017908991748655702786285091050652228738752404511639151645722632640000000
Faltings height: 24.0550
naive height: 312.8473
primes of bad reduction: 2, 3, 5, 7, 11, 17, 31, 37, 61, 89, 101, 362911, 247109339453033470641029123106493374824639961981730479740190319142248486184063
regulator: 96404933223299294354459839.49931325548088919711938711331882172730736172923066699537523387
submitted by: Ritik Jain
submitted at: 2026-09-25 23:06:16 UTC
last updated: 2026-09-25 23:06:16 UTC

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

(412495824046903606104442328940775040624859177808847706/517013399543546431995862910803225, -3118489548779782753170008818845531535618755173582870155753502913463647446413804809/11755813792769343607673094417626524880478412047875)
(271073542674748251767938470/97969, -4129115631768151467171075812344118277555/30664297)
(2464064969928111742142295/484, -2203989444991690208029937909455207245/10648)
(53406666477423098429130, 12265894488788349781142489453882685)
(-13383225771882950053274917095/2611456, -1659169280047150596573858343196811553663365/4220112896)
(172251288200232936032340, -71445812323662387910264470681625065)
(-404858268246517254816183859965570/87220399561, 10660288713877046763003213126570910437565615078335/25758887822749691)
(6183726644777148155717131968/237169, -474239111755299384212741739453998425433109/115501303)
(1530977082471405175211152830/808201, -137969432450361359109105702924545349961185/726572699)
(-4148807078605604955978, -426166092476918577853046860031403)
(1364612964872444281938870/169, 1256090905391099069509633659323331945/2197)
(4703151541334076255630, -171128818589020936339260589212315)
(142401722316275744028870/49, -43842396337437710716506956483514045/343)
(-3878088223058325368370, 429744302200360238888056806035685)
(13549796624252069416440, -1444082917575581909678535683456565)
(10144657008819845921766432, 32311414757789620433215472115779689971)
(-2404496364124108032020070/361, 1542043447751568766220775623647668915/6859)
(-58844790588241208798544747334627254810/25623430318679209, 1702691904305606784604133878272538749338392061747120182695/4101624562958291714136427)
(70383976274767754137036633713470136300967582751646120/23386005520627897352495576827321, 13953281842725754868769888632771034174332802962497075512865895658244589564454495/113092569580123488261528449980237834462816846381)
(-453563325058665983198462965524861897450/92557839373773601, 11375211233781010574773535362101414356631127973892598925115/28159167565211299333979599)
(-103220742750995533821465829183355410547322/14631662075327326969, 5465500899617901132235621417131195814354593989270153304262959/55968090950132943254850898547)
(65432529542545610623790238699847787291805/34537035362232159376, 38538112364199962313596503978114170905106193922229334094947185/202968004948951538411595309376)
(15427758513538926756371692112226059435658343981580/10053302516798812810796570041, 216649578268176228723999201155108456628573872516302148055839716130544433535/1008006022417249416653991613428227075155411)
(6304660369232411350330362839663619975448627066967641273746861255361850082/2106025454210675589604293886323924343737036896618161, 11987056316127617160870886906963569258300367834543632276408067804684179585691553671428423548992910335477746027/96648568051410751216460748418901974258164197983768052106122582691331173469591)
(17128538528776131255775914878345142828102363462470538345289460212726128486720/17239642728803305081604281458203024776045542831073833289, 18051146684257534373802766523827815149326980091507794735853412923666621370859335002313149858330338455476929156895905/71580115037199701886130235365599722316249094190475316942703017230066528967064121413)

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