curve #1388

y² + xy + y = x³ − x² − 2167206242540225241998501189120143052401049897335805x + 39143445242357312258290877999596739647015703715955681339833673743747148822597

a-invariants

[1, -1, 1, -2167206242540225241998501189120143052401049897335805, 39143445242357312258290877999596739647015703715955681339833673743747148822597]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

532778807262776298196629275652102696263093313041144114295820054048761256062672874071719721657948399742887560168948187729871261387650

discriminant (Δ)

-10464998141854699733904802968022235474294765523104843012484273180487301880228233244605412367358374891912124033349741142537679344599359633600171525022720000

Faltings height

28.3755

naive height

366.2454

primes of bad reduction

2, 3, 5, 7, 17, 19, 29, 41, 59, 79, 521, 11831, 3283689259, 174715485271193, 138161945224727653946137292272760504949109, 193389032003160642435046540339164464702953518421

regulator

16005128659664004948770157745491699.3363822523247668432213778471766410400994879142745022137287143

submitted by

Ritik Jain

submitted at

2026-09-24 21:24:33 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 04:57:52 UTC

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

(-277911594493204017514413093848064235820287632677011502572476401/5451886034281859047152552967989740521, -1667501330206045450413845896454424661312963584742188538118487365514826604802473060742310195360/12729758166024933256650336565072281859917416687439415819)
(27869889868569145094202419, -19774901134057504800159012386754704380)
(184446831315598834127157009679/6561, 11091042774802810580284707236271820244832200/531441)
(26960140388683547609219759, 17641325087452413967759753290475478600)
(1073833473284579650012117367191/38809, 145415228566263454769991476041662222706142440/7645373)
(-51775653273963272457763241, -112053667748299497171829403308957279360)
(248068986067854709484522969983/5041, -81352736928339300167798272119082708528618760/357911)
(1500435233558324908851203545/64, 17887965781783139225063597652433495118881/512)
(-28703761163797294514379680207633/543169, 31252522531183051897274667847690085542797255688/400315553)
(-8551007221292872825175141029/529, 3217972002918396962171827469182446340289240/12167)
(29492989684609208077268569, 29667002793272702795884092979372319420)
(58299896796635660180755879, 333091248213506795971003140939289451240)
(8264066555116026645795235, -147641123522823366085453668698294608504)
(42841692739720323755446399, 157888441150819281903855890041538920520)
(67426251332476729080271318039/961, 14364153246935767382525224219305266135252480/29791)
(181389124964441095723876147999/6241, -13106241969033533469617427422834438312031160/493039)
(80154610530003281658566854453983412196959/2938298133257041, -2865788447881030096963400262582472218205337654998917729158920/159273597230498625695911)
(47489696527820628945498481194678234157133721602993831/1585080731518393497701886049, 2099019463064975599648058526599258986787864648685900020293069676620128455338520/63106933875826974562142390825420981415407)
(-952926943084043403779015193359057929763073438133597811/22516707188534454514673045161, 792838828763524282876741457478151795342418671760553736108560813710388428609304970/3378759815159287377699161410159861926250091)
(14324803221372999997055466562334629261620380867317951/587605817893126928180739169, 402556081295050204743104217854220023186667278298782997731791527772314054410680/14243907038912212674269922797001155006447)
(261011064583141918876164257044132017821911/56623116473191129, 2304432266226713121229713960699215482304046288864074420571410200/13473817268137994494832867)
(11848721583385059325339848290779/450241, 5536796865016454007121964075859148297116008920/302111711)
(319173783183842118541516471884769471/6963068025, 110418762564636346094735056772825881987666342041865096/581033211346125)
(2809693865351928356501279513185261250134072418900171948068775401/88462840455811351649511198991678392889, 40337098579849511360648150854705009412633754778059101681554166505403322646730973553063607590100/832034472266382183697686333371919371093939851348964128787)
(111540525187272069011788859221/2209, 25101230363405295872385731496540330482302180/103823)
(-165545681555041497617922789983837545167942119921/3584401907490017293681, 43304443952858478406603166295556960090414090561827574459988976989339000/214597693402048900455106145495671)
(13288285401036995465883948584324683942486268573495841991/7148479279672144923466559809, 48424875463949140252730439540636041483676856188989864978653084878622514246250724760/604394486677917299505483409364798083694623)
(-322499067175584893166656502245934806489/58126702583569, 100077134382750266064287358804291283802768372887395362833760/443163037520254826503)
(621078638559624371390677656130645905437385865612015/28857597927673316793964281, 7703776734205994276710300081955453290517099307784611749927915003239455525944/155020904720325836633289602902603096179)

Commentary

No commentary yet.