curve #3577

y² + xy = x³ − 59961653528220816290860587566443594772699370670850x + 164446790187578173236288345372345415333638699757166940580441894472574043332

a-invariants

[1, 0, 0, -59961653528220816290860587566443594772699370670850, 164446790187578173236288345372345415333638699757166940580441894472574043332]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

8666485118476502221611291639868286644432426824160317076637610325975799348351402548340021603823528035309908953945462669270

discriminant (Δ)

2115045235808488855189005240866058090049205499321841724204638577177949521252986847680520423130558591588727131249246055157256780330578844822960000000000

Faltings height

27.5848

naive height

355.4670

primes of bad reduction

2, 3, 5, 7, 11, 13, 41, 101, 347, 467611, 6459049, 184395687860047025893037711, 360619244560397885292159755098464546887334181122169827397655692917781823

regulator

720617873269574566653791033051372.494407016827702464857117532776966696730710170038201993730470104

submitted by

Ritik Jain

submitted at

2026-09-28 19:32:31 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-28 19:46:30 UTC

Witness: 29 independent points log in to add more points →

(-2116420019369023405736475759944658630044/10296306408494089, -13890511725272562334822048430346629302153642062948979781467226/1044773593721590101091813)
(3179601014155803773168404, -2436798150042345017727951917978029202)
(18238915638196557539733868/9, 193299129027781171805941974547661074106/27)
(28540034159858278485137404, -147309044145859358452155977369601097202)
(36981648557966287221161292976/2209, 6444352290841155823116484307816183832939794/103823)
(341865118059794275475858309416/49729, 97390010785874319651102143706174105005779666/11089567)
(303010932264929856648739636/9, 5144835070264201261416610657581076603546/27)
(161031707785682280640584996/49, 582534070378684511102284092492906130914/343)
(3905817234592730048219887547342231799952543571416813029927684196/82885536818985074454818363998550703649, -240976191402462994564081615230816216188943123774030161455917081745431989301919701127410703686386/754602312672987219019904687359806900474452129744568649393)
(-944577064898751651596, -12825888998016143276893814120144989202)
(5478430984883511165143404, -613422861762060181319200677877729202)
(594607296005694931782007118481/53824, -364116393518581644255351827747776018382819091/12487168)
(28568586597610350544939151764/3481, 3081530671942184706229972096867952001320522/205379)
(36925545816644609114743524, -219768427172893342322057515758350124882)
(33803309294880847871023639/36, -2254814815308415436744173746570444058237/216)
(-453986632572640468028253116/121, 24419527775329709055072890752754899892138/1331)
(-79130910302393010660116864/9, -93370503925102734797096035425289368454/27)
(9370329649038197887079875827060691218091564422531179122/2759796698339147464126978319689, 78274993551944746711714939362432204610728396228740921218544752255777335338507372/4584749756532173820214232443185125430269101637)
(426505823149881131133334721884720928124910395792541177119047932341258490474270889716/77346718486075030296206707080205021711730056033313066335729, 26111349641014377077982556339336952973703456986034872505191518000447105324904726182945375102708421419896711578395463126028766/21511110914102391228063889520514042328663603321987840220057310912823468177025958560287817)
(-2352897234490642974097965525101384/416690569, 152867103615768403698159017296668952924878456209026/8505904584997)
(19691698003624494740095188314612299600830864/5997166021405038481, 25281827445277090848339337203056785256020899294308783510907655278/14686526984103744279906540871)
(4609500371763784235708413846948082012230636016116847165101042306575505062891598377989051415076/3635900948439096722475862955112075854325271043017803126665839606912369, 2085269546273210426132915787490261691029102659866539195724118474319664512553901892583387699936017793917881380730674335853529692561624054503906/219239127508584970163551683547367307772452608251461078557536713715955272422638260141676269122807141513847)
(1800360903295477873983780902567944939764943943642045855479/2462064417556031880546311283720676, 1343774481070587109754302578411175521184415448019581094894769942810860821842906705520023/122165652083042082092597408316381226907993683847576)
(12329868589988121186262565941946217205834830043186/2255410602439339196147209, 572224895802539814901902848751950629816890253337460961628092851215444246/3387181171212634535889434089827142427)
(9474185086042575643192348869496739499459104340006250824376072914271096427597714889041687974098513115372144/1574097340306779071797981651436379921949625959445634816444985802076405826867849921, 290161351468315994513065655981766129495779079678753808407412529860455184423846368700426886238456793688937875935556198970348322988097558326882515854990388855298/62452147629718424878729200436659746352911878304739101559114132860374168657337401935746587741219621284202043418775239669281)
(160288935236219642652399944892818278093154623505882115236453126135861284/14233367684201912362898578629280922184812053681, 51432451142334219436463455342793542315139129193690380222834497266387711477554024419946412577831553905635938/1698093121009312061433706591751465566445470967192229936222313088235671)
(58302641746612892867859242834470442074514560241733645491211321526276/18191231621561224312185370521725396021244169, 176790123546577836996249414313995995716735308773485584086440114641154182390182432838370052838490639706/77587749575530337760136674298255457949837802426924793279512353947)
(-40792930988203981894311673104327029507438514564330440385060005342366/8829727159892576076144664003690423568850721, 485823486779738735455853284614237903266704993901169391005451718048231813210786121071258211438131538812/26237407833907407331529836946656783715006513229550752542587678769)
(-1034254862674300334158301467085740281138644886550766037838220774971059217464/117811149015044821526391137799885692946343859566009, 4828569081919422314484182818261508419363322176402982242835005393079806162891332734537312987696808370873841820246/1278732159298028744301686055490579216466275641374896947741178434484572703277)

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