curve #723

y² + xy = x³ − 566516494741485099549209503021491787458476375135717295x + 174472250193582359895869067484953224217833831568696892188505641788985771182849337

a-invariants: [1, 0, 0, -566516494741485099549209503021491787458476375135717295, 174472250193582359895869067484953224217833831568696892188505641788985771182849337]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 20055327672089400737004407935464782012169335982105417967212322048377233319115863413109239602050979277196424547683843421345288310
naive height: 383.0500
Faltings height: 29.8679
discriminant (Δ): -1513951066581171546499433936294271267355790086602521552792074071778924707835905279484447058052052481763510555216085941920170797629531234194837715790480633600000000
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 37, 47, 53, 83, 117671, 27631103174897, 66148554958831, 1112422037707502039144188394872166053, 8141586433360301765294462245338560933444733179
regulator: 538047406483686218254889938628880.8823765776521039141767793874265362653684313999892021009854872
submitted by: FNacc
submitted at: 2026-09-12 16:25:04 UTC
last updated: 2026-09-12 16:25:04 UTC

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

(-322703117384237174690889306, -17991204993404465000966151074652774533667)
(-2335091569047854162210076633524274/2839225, -43871415414703977545603663815020259703455260821679/4784094125)
(49389067385056464127276364134/81, 5442473574494146372123293497603179518466997/729)
(7266189917611406086837586877/16, -210885052625178580068917898266709215882973/64)
(434371144506893929042020414, -3217178464781235673339705679033030418507)
(4673902823618048112070559026086/289, 10093868741334788406114690320713104563828387949/4913)
(2620327227423958992592482831/4, -73527912921208672831343715832950950385831/8)
(507150819048857241306555894, -4195608077323803031270105218242105761827)
(129167674440189297410002562166/289, 15959507187429577121315678265056936997409629/4913)
(54183158293499103782798941086/1849, 999059146543974877533693734710865630209433751/79507)
(-124251058693660689067134408, 15586670463381715479477565513669047583203)
(-865604120523728785435077546, -4034803074998249837296767277623524708067)
(290317736590459234636445814, 5871261917604506730444571504023040348893)
(1694087023203604210350072774, 63848700889381165939163924113325874437373)
(342732827602402688041948614, -4535177262609350996666140201681193474307)
(18416797162591375993976789007936/289, -79029822997033478190783266258310590370576397701/4913)
(-870296143058654383873483386, -2886813048690219155649900211198248026307)
(19417954603097559946549550948091/28900, 48427335644597936827011400555093072526413840551/4913000)
(177492283552704943853401461400661/300304, -1117433850173329891348337348393207152868348493329/164566592)
(98002591615592173629797317078165302/575088361, 125552382024515959473586668487192930288681008845741793/13791193985141)
(13952217943540209344552280366/25, 708539229826586551585386709028666963143449/125)
(361069459675338532633698864, 4122315845320775275175288690747090548443)
(100012495008809718777468987149814/14161, -994740347862166837646886037447347855498752452293/1685159)
(2903889211430454342437312086/9, 135736269062053530847829733893256696362191/27)
(90772412265111533478262596768792/380689, -1709138636539223501084710554543989622799463783637/234885113)
(1744407537871886294080482831/4, -25741250720547233723072389549565241579831/8)
(2532145079482223010016404831/4, 66706041635804239601928978247486994715669/8)
(87185738094520164029144396134/81, -20769913796360356703745028582914412810416203/729)

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