curve #286

y² + xy + y = x³ − x² − 11525691028496208487693310738282x + 18833323594165105316445398903949581636278347689

a-invariants: [1, -1, 1, -11525691028496208487693310738282, 18833323594165105316445398903949581636278347689]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 178872103474086290116257971972938572215182078046668234704327697980888381040890
naive height: 226.6271
Faltings height: 16.8918
discriminant (Δ): -55238036499572174457018031144729080372840647735935725107263389724288692295039993012310400000000
primes of bad reduction: 2, 3, 5, 19, 193, 313, 30133, 145063, 2052244018292853705583, 193026453955572059145432582176976218143
regulator: 2907969023873116426967.1791178455013156032121181031273999834489064949830162442403
submitted by: 7fff-zip
submitted at: 2026-08-22 18:12:50 UTC
last updated: 2026-08-22 18:12:50 UTC

(1898855732881497, 61598003548866302046751)
(8020374089989226062513/5329, -718275138333175763464254176451233/389017)
(2498327549095567977/529, -3213045674241737799694862119/12167)
(42781922736996146187393/7360369, -7687650651318157450817764826879153/19968681097)
(16694983102546958961/10609, -74054457643577953612084308911/1092727)
(35860082783684295422793/11648569, -4449694851459870570447413997939253/39756565997)
(353309374283531689/1521, -7542751447036491319605511103/59319)
(229080730026107923094817/62710561, 79265160722401771726552329962250809/496604932559)
(15181798083499965441/1849, 54954845004059730377604340189/79507)
(248813241420759796631977/32729841, 113981638035002929876413729736877111/187247420361)
(2021050064429697, 61600272773368671500551)
(277393518887835380369787/117961321, 88147682876987294824234686501269131/1281177907381)
(26705213550430497, 4330860469808857481277751)
(-3209515070606403, -150877530412859846254349)
(13236899248325888067897/4239481, 1006122664814942000937533428265269/8729091379)
(-1956294518662503, -184103388516250798784249)
(-470630577031099353864587/348680929, -1163453861222622044128719848943834033/6510918987217)
(63902608404884173507/152881, 7095227401974646461440766152971/59776471)
(-21353957934134299767/6889, 90003058555552816922085667037/571787)
(-2664274899095605871163/808201, 105300257258099833843756462665089/726572699)
(-4004636205933024774419967/1050278464, 2917307961366129856991221387966447787/34037424461312)

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