curve #6138

y² + xy = x³ − 1855830937696521398473353497586531787070230x + 970687863793327268334711621146668265137600843626250366783808036

a-invariants

[1, 0, 0, -1855830937696521398473353497586531787070230, 970687863793327268334711621146668265137600843626250366783808036]

c-invariants

[89079885009433027126720967884153525779371041, -838674314317434759841324460498235530619577210344906547189879199665]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

561710137242268268883502413967535941353786404088066933983739309634692254221990617175792565996277995883498

discriminant (Δ)

2022225916820889088833697660314850669509800574148905233251206702734963606491961437580403678082218437192813954150326124444024832

Faltings height

23.1072

naive height

303.5943

primes of bad reduction

2, 3, 7, 11, 17, 23, 41, 47, 7877, 63559, 55055233, 5322095004464475080632067734146756911047500951506338054514302926937000599624883

regulator

110558070819544537651159548706.38892415038562363909477076714740968943238161213713726976097670

submitted by

Ritik Jain

submitted at

2026-10-29 13:47:29 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:55:33 UTC

Witness: 27 independent points log in to add more points →

(28769151607021668042204890808548429812821655115297/28988734835873780579325067264, 50902220163819121095638569521866102166250521080549979731217777420633071759/4935644743103097130630789932210378231513088)
(751585218849575973026, 654581695336446660938132928638)
(-1336071567630767390593444/961, -875429190624944572198179270763471642/29791)
(-1409677129315509865444, -28027032472232016304984987206694)
(308400720079507059278, -20680439270824165506710602987426)
(848471361289469750780, -2624136518086843501101778876246)
(830257681423714908802700/841, 244778012208621950997288068315819266/24389)
(909163107169016223356, -5910047438017302260834945891494)
(-1039677420489518005855132/841, -904568661917660951729042164411732574/24389)
(435870610564856911813/16, -1941376147022070503842603504886009/64)
(11668751915174599598026832/17689, 13621246061581426128691620854225658398/2352637)
(-1479265198593264922216, 21885797096074808366229580006286)
(33688229505907970444, -30136463593214875070326898976550)
(2669237746499061932675/4, -43398444780220674115096907949473/8)
(45647541490187938491527564/27889, -224235336478337275881686272588995583082/4657463)
(5090630357726487975090686/841, 11216803746632950779360340044213260374/24389)
(838454709915507253054177/1024, -9549249830909789398238417883349951/32768)
(256091321773501999634091772/106929, 3542299764207303982569180941781073516054/34965783)
(48381508152998333324533892/24649, -270618492421297661929215311833715736598/3869893)
(875740420284147288188, -4133481071881851620526540543142)
(10300374168544845357290, -1036677879464745352953780762990664)
(866058453869148756380, -3608768435260613436934128489334)
(581372312437999698164, -9394645133962741912743722702854)
(135527236653289490485978004/13225, 1564470967916389850942106936646119028862/1520875)
(949430040554361744878876/361, 819680679617421546504504430863020942/6859)
(709490001673335033854, 3336862614272170087954324442270)
(324486173550483709933226845463070850566093644312443539006336973700363259480262109014465384964/482927525512019380314863292996425287807492238063621622538930391630422201, 1746304803554032040682179506338935642909438231962106277114599264997436258081128534479318289137728845710868319290443241974850062307225981190/335600762973040307028419273975033259063868000627219454407611868359315903559870960484966873795468030602292051)

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