curve #378

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y² = x³ + x² − 3896830274733436253799445060729628270620x + 93850226586476646888800893430393312604104981963137354427600

a-invariants: [0, 1, 0, -3896830274733436253799445060729628270620, 93850226586476646888800893430393312604104981963137354427600]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 1747020859333871543900768055870997670038160232551802166940227186913870258717185911179254594920
naive height: 285.1012
Faltings height: 21.5640
discriminant (Δ): -17830783920392527513466291341405486840148251793028291837629168145779864016933504222533041779349985742117057262860000000
primes of bad reduction: 2, 3, 5, 11, 13, 17, 31, 41, 59, 67, 83, 492031789, 29186919876703470379599071983080289081320265652340207228802411076543581
regulator: 11920581861713550426505021.699409107957251228684458633777935659210873193624789762585497
submitted by: wgxli
submitted at: 2026-08-26 13:43:57 UTC
last updated: 2026-08-26 13:43:57 UTC

Witness: 24 independent points

(4977253072503651248733746081851011357852734690/32592372215799015547427809, 325496317989898538372638871796917938956233883977366136374964584012250/186068971561757864473075998654204030127)
(-23281758767417573098340/361, -1902365933854028392436352709286100/6859)
(-26006132699808392886640/361, 183712383586460080722296988317100/6859)
(-7537894403849328157066/121, -409905543969013351942440547384530/1331)
(31836696205284275255, -45353186153562884658803975970)
(4670264214837200411112430/5041, -10070471685728618841486818394304505730/357911)
(-54011312233354669700365/961, -10959270044227964436500984043841500/29791)
(911471900988087415929820/42849, 1272525396269930183226608370495885140/8869743)
(-376225211245835550420082/11881, -557757338133904218329885683671998646/1295029)
(1891280282981896343345/64, -34347621437350838943408504315465/512)
(477554030667687836494310/11881, -60152432037405741709451608104279150/1295029)
(153464064348473711830, 1763545465749080366507247852330)
(163692601291598279616157565250644240/58611319574809, 66211892155809358069318863575303251565031742473713100/448716716234781466627)
(-22999369116109428439481562535792885990/575049069219370201, 187929723115333112305123132515392346224107182656383165350/436071152090476819665929699)
(3406550941667463209348678/5041, 6261494484259928625759248681970200106/357911)
(-487700670088729226206222664641810/6782133688009, 833248181606860416508320278720316797178879165750/17662392003398502277)
(73103603596250510471762510/1968409, -51793642824400827658429323219048189510/2761677827)
(2176011578788901752788860/43681, -1395047236559487100864053339845628900/9129329)
(633074957385337023586043025137200/8211440689, -15928781660193948910659614695219632562233921583980/744096120915113)
(2435565412742877098719750750746834038967888185630/18825199401242874731494738729, -3422038147944551782537886051883902395616119058698066189118727265008497670/2582910617826665991924625078059355207185067)
(326719135451835127559058728503580/3458770489729, -4850568986564992566533400888734510715405208411980/6432541805076730433)
(252228300164003811032283458905097660/2968380835156801, -99200231600537140423417924198535038976834651438386500/161725844816341880206049)
(85809645152925077317782896765586726590/2359800440144654809, -55145531574810798056603413233979146550872866184757960950/3625040948215060218509673373)
(7775857596859092441747577281890/190700776249, -4366884050459418561680854172385232456146393150/83277694082504557)

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