curve #1900

y² = x³ − 1009191665104313290271509664885399234998767x + 393598009175647033907218224282077492537357664313859320432985874

a-invariants

[0, 0, 0, -1009191665104313290271509664885399234998767, 393598009175647033907218224282077492537357664313859320432985874]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

755382027260343155558285807896913965115787869923215653132154548840083006992945239548501138162055151703256280

discriminant (Δ)

-1144106852725848884373103253714845690622588855062284290570373078706720586201831771245400999847922601864789370266055868380000000

Faltings height

23.0071

naive height

301.7840

primes of bad reduction

2, 3, 5, 7, 11, 17, 19, 43, 49037, 588779370259836383424158570718094215523, 67955711823190452140776503295430496463633559717367171941

regulator

72591723122321934341097081191.7384659250763818897287411723334002092737575060221050375896761

submitted by

Ritik Jain

submitted at

2026-09-25 17:48:20 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:53:55 UTC

Witness: 26 independent points log in to add more points →

(2682142058078514941654262/4489, 595232364370388813780178511893568500/300763)
(-15383785932209365235022995569867265689578775647/68509484671259551098397696, -13992497495930388907947130311245122980575072560137221951376065283805455/567056131995394558815473299058447712256)
(7487555989141051720001073/11881, -3638302243212078763413731945331770250/1295029)
(1136561316937905138459705/2209, 337373971461018264451519230565715694/103823)
(47618543748533016805828017/71824, -76838462908206144922453183485997912425/19248832)
(70253788297554788201633043/10201, -582910120010472151869717313171609320480/1030301)
(1202977639370319247183, -30339056503246441963645392471800)
(-56180835046856158704995/49, 2261341787469648125368813651086254/343)
(-1060236188184653349462, -16485363592948501098086895281010)
(14102631173698972981165729/225, 52953513377942324978211406986939868442/3375)
(-148864114587346911375/4, -166104462490208898944623556370831/8)
(32256122876356486886937/64, -1845261032007575483645572362476925/512)
(857539812159686952027033/676, 597264156193748064097214685562767675/17576)
(137093472142294758603, 16056806640085371242028753807840)
(-273013957200030914692939803/247009, 1546919346230187777543338652623646943350/122763473)
(-192925062020797574439165/169, -16730697748885190892023762708761536/2197)
(74003613999549706601788150259887951437/348934208128880089, -2834425380234943233487526891131007382508192921440738660750/206117716328911174545921437)
(60407579112052970254189623706383011583338769128396517/92436459782858161377447460364569, 3226123893508820071230055178082156150131968671661610416147963457066867365535610/888720004929495330669041045980877301382800127997)
(-373634239858484273217, 26804967431099610824135741556000)
(36681932682077794903440345/63001, 29105114645943236342848860835177616622/15813251)
(5264910743828873320645953/6241, 5887671692018477382895017578482424250/493039)
(2175496050169363545884380606998523814308401229493317/4307288744082943777064087002969, 31889792250787245931288470627820552889682745375418777653762060676104872673510/8939350778674933327734959949448627895366936797)
(18862889922337461046744869152537523653217/95818572062518722769, 13348989137753610658663045782763756904946624688896474848834490/937938886201233144059084243353)
(884362041783260001732615789499375026181791952593/2746137672169651071910730896, 1453377993124170094242824248232060869433834272033849520372493480807852825/143907510053285991400014578530443341594944)
(244714615764582966771116306892734889415859976561/3824202596205478014841465932025, 148354988214071797365061745127539398403463565210578226352686837289574509582934/7478445585362662519969283992378704261122709875)
(22074366903367924910348180932017/55839107809, 99114750013045670947695559933954674542515471830/13194948692590127)

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