curve #389

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y² + xy = x³ − 1095282788134949493900735863144922358015x + 15295153953560099274066571309175569823788527272931004403225

a-invariants: [1, 0, 0, -1095282788134949493900735863144922358015, 15295153953560099274066571309175569823788527272931004403225]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 98452346323693454548291780481483852252722663233212833475675666887853865458141727050829822570
naive height: 281.4729
Faltings height: 21.4222
discriminant (Δ): -16970039025550863782887325813264596680915050443093452753907786917780581431538468373817152988169621651380982872320000000
primes of bad reduction: 2, 3, 5, 11, 13, 19, 29, 31, 61, 2791121, 20961451577768624415013, 376465889677167436499674830349091715279203124660121181
regulator: 7571733996873122022843756.9773312309816999665602799184414690098214842820345712230933043
submitted by: wgxli
submitted at: 2026-08-27 13:18:22 UTC
last updated: 2026-08-27 13:18:22 UTC

Witness: 24 independent points

(2393249418515381842646673305461272900757430/103136903618699611361281, 1613893473337073806071988254722468008605818952879174509134433485/33122349335485453121155547388344321)
(4618289867064402230630/961, -3000254985357041926723329426433165/29791)
(-36787987843609756450, 76165333003294431110481685565)
(108838093100436131160937370/16265089, 5963810104695512399513906033706340964945/65597103937)
(17024429570353555430, 39784421017960735696754219885)
(557739062710559165246, -13149216695037663015686682263683)
(2936972403971915420366/25, -153499948006437356195692762641551/125)
(462028508557065717494/25, -4618846603482624699202440025607/125)
(8536714861674897600870696962382901430/487834879206843529, -13140060548399522766542053053988530613042305382295907935/340729136313260696563626917)
(53589781588071338461359350/2217121, 179081016777402082059248838310971452285/3301293169)
(311282896396617903557323859452310/8055260036041, 4004258502545377175673035526700154042569606332895/22862269873830809339)
(326604362242578064251974172907430/19306260544321, -3401274707365711396122509544837343105597755037235/84829565836826054369)
(57526974447641294257974605/2521744, 187008295991647407798916850272051274345/4004529472)
(1683068021605569450923744156210630/213289054327561, -263276381402138389275549493632501256039807013879585/3114962717513464092059)
(137573173665136587670/9, -1244477909955674933296541565505/27)
(12807864986127282585280432586/810825625, -1015714708068558988857655998452949690283841/23088259671875)
(701225264287917053990, -18548626585800959122190505526675)
(1394325434005406779783466590128960377017026730/37288522692112773206736121, 37152875351480251233331068913224962961839171016305952818746960343485/227699861545515177089816745459322301581)
(1774146674528316356750460160928837830/89473099244614849, 991803463253933320607556063601152866908054480941256115/26763242029942083458743007)
(100733648878502068679131926198230/5944482773161, 579897164868613255772645068255255642809929376335/14493427728209802091)
(441225575912765424783206926153875182/21671460976865401, 120852477341876953731084588818180553949340362817068703/3190305593093141494766899)
(6663564960648759715126381364955465614630/353753047964927857801, 244220704678300000144251460015200922295515691932270450401185/6653501907090352037619277601701)
(115553302548929261587467693615769145437592642870/942070899871323308793372961, 37992055585127841473023658938552507724346199296306223645457170635038035/28915145584733283588513022817514565827791)
(3032168430960671060247640057431020886654480170/50115464245161404583392809, 146499040072242243407519248572741364373802986454527181759384913223495/354778780618099425789746948831575747627)

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