curve #1950

← home · all curves · JSON ↓

y² + xy = x³ − 12571193076409462488441265633052934110x + 17441265343790102872198999501828538196977291971321022916

a-invariants

[1, 0, 0, -12571193076409462488441265633052934110, 17441265343790102872198999501828538196977291971321022916]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

4602946029136108141523873485353131236407127499471409949595324492274524550729951398910628656587922

discriminant (Δ)

-4265442618478765456518816568473551798026602898094923592041794075851719332646349472698319109378356056351272009728

Faltings height

20.2134

naive height

267.9200

primes of bad reduction

2, 3, 13, 53, 61, 71, 11955139469615840995033, 62418253137705534986846246033, 344517248080551190748433713366607434737

regulator

184577497099005559776079478.88372894366887290950495731117388688280542800218610093617535

submitted by

Ritik Jain

submitted at

2026-09-25 20:01:28 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:03:04 UTC

Witness: 24 independent points log in to add more points →

(327178859291456957050726942576400253448168348/105566550695148672025413001, 3115351776110410248293974386200572547197759195764721668004689114022/1084649692156741248717107446691873505499)
(9849539513769999919/4, 9521090979711188330754111533/8)
(2056013205094329244, 534682569443721809220624466)
(-4100162229850354670, -236674467981985365074145194)
(-15013205678388441196292/24649, 19299932258050816580285257563704602/3869893)
(-886598194383496984964/529, 70739042311882649166140698427582/12167)
(39022407174850165236603064/20729809, -63126947924557892570764436639721740218/94382820377)
(2134059885827027728, -576668676878291191714998542)
(1578723147745404892, -1236765525521453861509225646)
(49837896341824525329610/36481, -11694787238366302774982997392897014/6967871)
(4879908225185314417660/121, -339618084034919642023512407533354/1331)
(102612393632172166051324/34969, -15774750288039545788692339099601802/6539203)
(-3070422542962497794, 5205165516442271290628162188)
(914236852845090220, -2590822851348538463873041214)
(-46908311416493412, -4246275493503883999583269806)
(6563002208643416789445813874/1640331001, 371042867965495439026152100590683533654600/66435045871501)
(158270917676532020089430056/26388769, 1702824703403853757114281123627038428978/135559106353)
(94234808080381588244344595223295028810179147114487984125858876/56546389557474202466928085950533797338756649, 449922431476690746382907165440325538433980780938914789894330624211101411472073990795015637318/425213771010362163461942830482982289425045985566257345691245849643)
(-154154369235185466277775873976770385322807022384795417584659163120944772459967516/15120462682989243090223860296182801863359970922905797835778560601, 7793390543711662173509168842283915908779134794311527105721586852011946256815638899891704366973545745615452450333550871875030/1859292087245168151510471861126336543959360426186481177910379447291179837854607144225106906024099)
(198569237652227389048650699374859964/115820254133415001, 37968715669077182076082177523903327724048650894435594/39416383096816539313158749)
(17865207813386263244754279142592800252638303669538/13052820307695130741832561271241, 78899549979102787194348870541103534267270733792074244128265636369052157522/47158126052469342758557899294773474933551020539)
(177056054462238486575997856898043345027839098147333170931039296782269/3657559476396038134756347552826579815358101144976, 2349804290326186662116517664002880974840642972056003858312480419444650565336071271471452893604813983509/6994989960684942579669981008893643214358784251511887626038756780289452224)
(-17392557961672616383879841708571682815130165215592797418765917613256954175562441809246215505716/302024939081939264960703840289568608993903942345373373328969465217324841732969, 707427556601340951340947532324931497009017726969332380458595839993949929021997540712089026834065576310795277424346726961556619238729846005934022/165983228657587123238192163533114582348605460745455758962814008149129653249012972242812921125753652139191203546265547)
(-4579489548798061522861604/3359889, 34862450909942510500885405783765006210/6158676537)

Commentary

No commentary yet.