curve #635

y² + xy = x³ − 736275993777524639212058086307718827518424005727353395x + 236460787495750483793685965319691064891511169565071192116367380569902358335277025

a-invariants: [1, 0, 0, -736275993777524639212058086307718827518424005727353395, 236460787495750483793685965319691064891511169565071192116367380569902358335277025]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 10611483916571002514287713355904577915721002528082815600145909332427283297975576122739595921383606478642086875462261937174909193664770
discriminant (Δ): 1390043918718815135469996245601753287278418184236083220029598093810234261782932889760212984112819264444525897052068138418307972343652111633967831127068558080000000
Faltings height: 29.8872
naive height: 383.7139
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 31, 43, 47, 61, 1699, 10455481, 4157426085193, 54434366988506808806427083875088521324154896450993280124197559455450139904801521974539983675371909
regulator: 3434664801421129234764751200030869.174570506610239478362332417841390255570178738119956049268870
submitted by: 7fff-zip
submitted at: 2026-09-07 23:05:25 UTC
last updated: 2026-09-07 23:05:25 UTC

Witness: 28 independent points log in to add more points →

(561210990607913885365450530, -111234544745877821268276835067726809695)
(2764410017544038207193693135/4, -60770955562362582251308624795192469220135/8)
(229743569625540704047427253150/169, 91850281644285238807684738076848524542421165/2197)
(-698375089293784609572307698, 20249461195803992217699611080290065342361)
(637070554719538358407742190, -5095270452140174788213006347944522797095)
(882607943389663264238649390, -16557973737582881118414714901976038141095)
(373174713987407387579194590, 3697198752011049126116436080455744592505)
(-6383832319617319451907450290/9, 541238251990158430412857291984551947882435/27)
(-221473997474584937400333810, 19714545733675219690822799925774220138905)
(-233466778553108357200299150, 19890481634817199228190502777831573192705)
(391183666321844262128846790, -2881387282773209272670160143921100763095)
(424554410020094730478022126, -629278426882793665992682709850137128903)
(774090890168299398272001630, 11417724887261308493527637485239018685305)
(2997875574145990764757495170, 158024928669309248624408570756839655360925)
(39841626459707163868563293310/289, -57626297804412968931462110759725510732995735/4913)
(677598741481844627088419982, 6976662797734869046708398007952051593881)
(1672083123279451221560932110, -60665144368190163947617193890075695835815)
(425198826021042754615919190, 520109195372151643403658011567501440905)
(3828951772904910168543861310/9, -12778798201071097614124150396228678182365/27)
(4049351053813834196089302990, -252295893571834384683672996509362796629095)
(-354232967866306349640935116710/361, -25776765107160326880737447944709194318854405/6859)
(-7602161993142061072923326824665/77284, 377018938225188204882869874486088933416669607935/21484952)
(21599470576527303467140833611038782/56235001, -1355153263752372308945418796227847501871586922805637/421706272499)
(562926805877839698174003330, -612575970094729541120584706188143889695)
(373696001214229290695332440, -3674718232791773761214382216395034336345)
(3219772911065348633865937299630/16129, 20219518208335467420550637312096261409067512615/2048383)
(150947170845071052200535573608190/259081, 302480997267048234924814564573953133873774177245/131872229)
(-85083981768884964131781218530/121, 26835561172188187781658546775298437824209275/1331)

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