curve #6143

y² + xy + y = x³ − 2078446933635185872234847157526254380178x + 29604745160036513528061617353920474192055040220109075248256

a-invariants

[1, 0, 1, -2078446933635185872234847157526254380178, 29604745160036513528061617353920474192055040220109075248256]

c-invariants

[99765452814488921867272663561260210248521, -25578499818271547688394885573009023084736463745516131329866181]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

94723048711303534447382787478290910035652490511320507248178641037488078215345993224622821442802543530

discriminant (Δ)

196018762901053233650229042023956030226492015958905631394883592126144341887315877665567848269534581637341863429556312500

Faltings height

21.6065

naive height

283.2109

primes of bad reduction

2, 3, 5, 13, 23, 31, 37, 41, 97, 3169, 1379237, 1921489636149827533851636901, 7449777582665029946734281164909206849582730679102311

regulator

8578468509563857791172096002.77818691081862880102311297083253079315634640932225626983162995

submitted by

Ritik Jain

submitted at

2026-10-29 13:47:52 UTC

later contributions

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

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

(255245491764013445681726934781151335593517195/1790622160505133625783129, -3885650314612979912217715128162278592015875114792035016352387435551/2396105480212371976462350200364056867)
(429665302916627658691955/3721, -261690454046773779422299495393265793/226981)
(-31633975033644153340, -252384428528191365004629402408)
(167427849574081943180, 2091642063924074181347645151147)
(882948110907589663044245105/8473921, -23970402477178346554002052408008621943443/24667584031)
(274481147258930342005655/2116, -135666880156601021389551653986516233/97336)
(36329756907578124455, -45223311582305146707617302353)
(-50331280859984093545, 81942276483713261027165889897)
(5159162922653048311826210/27889, -11385213339464772648704100645996180969/4657463)
(2009832997763660782580, 90080127244016521345022155873272)
(3013271470109769005606795/6724, -5204397832469616308977841674455785529/551368)
(-4746835539055430200369/100, 145970475296225476675091973933141/1000)
(286597003250749364455, -4793160495191556606330581142103)
(158205012718523609659745/12544, 103216403138516326071732088017950841/1404928)
(195568128317857696555795/2209, 76259466981298620908728738680895231/103823)
(141681521351770629640595/49, 53323186404177731914885843796315421/343)
(394061948541256658452710190091787155/558203894542921, -246863895050447702861383989571882965355005760325665557/13188314443591301596219)
(28169913525169581095/4, -990082335339449017218277280199/8)
(15140909621878740215, -40077154036599968053998886113)
(22622878930366114385450/121, 3307913025265953053123647777536987/1331)
(605248001457249479513/49, -26158864690872833102216845197471/343)
(940003283616788801806835/1444, 909179857964903755752156157349662089/54872)
(-13878801534428232724870/961, -7088101448080870282661856369328473/29791)
(4137670983337321547545/49, 231673895551448043325635933095921/343)
(303582356124369940337345/1369, -163927520532597532296081903403234509/50653)
(-274082632951665521169881951270058310740338897382383359601058280059274128369805/5927733889962047232565644221689919874111453343887083192041, 74792020254334914644746484402061804526122886781074841187301470810819176479549243178784016041313459970614594646541627/456386772097881160834178614867992456700707936148772785227021138135387930070568949398411)

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