curve #351

y² + xy + y = x³ − x² − 250918915934128421340307896120883808444030x + 45913507617476434834864347970127139550348536547695769941315597

a-invariants: [1, -1, 1, -250918915934128421340307896120883808444030, 45913507617476434834864347970127139550348536547695769941315597]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 107074891532966945952224621204518299580433513793782834200723311032339736144704863470239295173450550 ★ record for rank ≥ 25
naive height: 297.5914
Faltings height: 22.7397
discriminant (Δ): 100389893869613308546701811159859691227781576244206369338508671540955995652620345723520333859478092487932034110317225984000000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 31, 43, 59, 2704697, 3369124490537472383281372744326098394132219698540451682089624352866416157407
regulator: 311925765177093432464263826.0666104921180033159332589563271021588177548186763358122053232
submitted by: wgxli
submitted at: 2026-08-25 13:52:22 UTC
last updated: 2026-08-25 13:52:22 UTC

Witness: 25 independent points

(100315850069306399419246372183405240151/633044398788202129, 1603142292727006527872105137878535160571602294961235699005/503675998099605284018018617)
(24746945256734572970729, -3892190301262900173378394824299565)
(364631322723553824569, -1703095446448488298877683675485)
(-133831583622620424391, -8780509116928923011991164464605)
(612433164123928952600489/5041, -1485328668256960279738692407917730715/357911)
(11908309099024407998885991/677329, -3591390428741828878899805668830226394605/557441767)
(12537350273391777258605239193249/980253481, 44358828978359307235941292370249754665885062815/30690756236629)
(98360130345211638729, -4710063332142047523533166711165)
(2281161183125158532632895173265889/48633039841, 108945498280898974500035328734847317581993378758915/10724995643095889)
(-181270145186425309724633829481/802645561, -216997812228223252183184996050014670014096615/22739751388691)
(-10387290886257875733871/25, 1107083207264716772716079272816407/125)
(-2636661635756306245313310155316511/8047780333321, -220114385600942616299363478149605978880440711019505/22830434164165345381)
(-131796184954792499747853847/461041, -3039649471919489002871235237881973551931/313046839)
(-6843065411540853701175797881098271/81323151664225, -5977352533330955435471115788746928842548885318465603/733366895703122875375)
(-563806217004375168271, 2856898605765265290053431718835)
(133768281697916962438841/49, 48150342705585667474263938386900485/343)
(278178903725616307622873/1681, -205867193276511944041834798223459109/68921)
(733200296640918134492406736972807503774417/2125174400622682476544, 62797165842531451860685612293839892507444428122556354615649337/97969719313367488943502016643072)
(2908183140206464608357186591420185669/3382443807405961, -4245487771594864886245438806972476896659722344704789165/196718808639729463893541)
(6538187238710064114017041140178585297399805/15771837339490145436769, -7178777099261581793275358803208516283548428980417128810971090491/1980721583810895637696194717189103)
(1291217076833812782943449709500593/487370138161, 45619387309097637542161770504362131858225817774685/340242353482819159)
(20430837620866521502322266931569481/42166931870449, -1689804414369048645778103361241952010469454692307355/273815483962470719543)
(1262095416969223582386281070152584371181769/2016593805029287488601, -1048359547751775796260960937213817298128120748985479823255390215/90558171115146768322332761032099)
(11220067838193310268350406954005/29651806809, -11583339176916212528971439709194481290028522881/5105952177089373)
(1497209405642355971278202713839666113/1338012340480201, 1671410282191714739395572472774792423186391707700976465/48942954038586540829051)

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