curve #3551

y² = x³ + x² − 23216523413383725381905745094816025397267521222060x + 43135967315528649041116447619129425396309076715962063324059133067120956208

a-invariants: [0, 1, 0, -23216523413383725381905745094816025397267521222060, 43135967315528649041116447619129425396309076715962063324059133067120956208]
rank (lower bound): ≥ 29
torsion subgroup: trivial
conductor (N): 17520269029530926089161437405849872143576625985318044755024027455380276629952648734501535879217339723633268979237181652780523080
discriminant (Δ): -2939911787433255721657151074061712417356000983755353885827044835158109976139626513710485798819765818075253329609811940031553740055284450823948000000
Faltings height: 27.1813
naive height: 352.6241
primes of bad reduction: 2, 3, 5, 13, 23, 29, 37, 53, 89, 2027, 5801, 207187, 978096109, 930816669883, 15824656786463281, 2748676558308079067842987942257605698130032779903299734975499751407
regulator: 107076944151424852540593455844453346301684.108342555124137594483858440014946591614917130455935293
submitted by: Matej Jurasić
submitted at: 2026-09-28 10:41:19 UTC
last updated: 2026-09-28 10:41:19 UTC

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

(2764848409257686484294643, 285254214965668257402395557253136528)
(4110010064325389142799546, 4140394117943016940056277752805440030)
(2399874502492592930977786, -1114027044417715372494871487290735650)
(-5073131785254203802879342, -5509169746443211674964065267653731002)
(326588670862372720921356106/121, -490125924090755474867998987916950997850/1331)
(1967913661053525344416858, 2251435503348144946923334734003449598)
(2568769976138387560270300726/841, -20682166856671764991428797718173786190750/24389)
(635018603985335745297789406/121, -10799871450046718000970997737675331838550/1331)
(-213364167282366433126349, 6933961944899139316952474083068237720)
(381482660821099644871006036, -7450368071752901889001583880958109457900)
(2368652156114987262694963, 1197268923900778682398517008532629512)
(23647844185897969573513786, 112776217829074579106390239708394056350)
(1435249063281768097431245986, -54373647070222572488009803668910516634250)
(-138927782608668961903388396/25, 91933808246221910959864890791214381708/125)
(1197534233092558909410914926/361, -11112115619291920092109956225268329238710/6859)
(123772078897282615772586025294/49729, -9731141324468111785096767850900003703855250/11089567)
(139128230732643566367591949/4, 1626080569201300173464504067864135616395/8)
(4586539085989481111734213434911139592/968761842049, -5980615481752789163556551718233154789832522630152232836/953510624369622593)
(47768933158588225436453180463774173390213266/17283389062135134481, 20532418355727622950400637307586490538504269877751466069229938250/71852744227711682230301423879)
(5252255720918168258266337043764366861106342106/1863557582667906790921, -24152774149250547962588895931137122680116782113458896885177229615750/80447809831597094043095177704219)
(94668337705913562446262001366749950001881544/15458018019542646025, 694677006612486531830877581357623095302629628068222384103591648172/60775804142960097835120545125)
(-3849272656000827775999220273913154375011924455654/2197138305111659675036881, -28842640076530989225912087353437741792934559483862775784160707289415521710/3256762536039496293522434146770226279)
(2945575977015281393659820313276195005165376314458474/1052326076361209528270261809, 9741807683824754580757466306357198322528918543027652660037965585522482047550/34137011492493630366386204234740360385623)
(2156983415076784750686802328072064766805441387195242/787002652933648519740422449, -6732825270258837865232052411885016580117959750862377463558180090079688110786/22078232095238054209096308007185013315543)
(132943550167355892661839863485780214109463324794868/2378295189663468236495161, -1527339146123312197654685206006779186217855792506916402177458756990583889508/3667740798308322279627463721093324909)
(1544647744008530621400007590838024213372298784629506/2031803895107045707397445721, -466320973495970530766606760033513354141348346364659372794657266323280927044050/91584648478871937444784859266863162330019)
(22191179022824432555665715767084299362462705432472853/7944696353760908857555447396, -200325180727086414392032748511214451328851175105843945506566268478292652956743/708134827991929682352648784668087966353944)
(119916150943577192550926511234451373265214752111889378/42912577134028847392950327121, 2518592590779545725525653124476736679692442987188803238599889855552993006790118/8889491020864077406488833675940018152053081)
(46303457786756275214094517359504341750215365895100272753/36928198892707086169874204606464, 897535323480613693848708040054881769142534194820820355984102083424609738457481816585/224407407924681906610352240240307184032114802688)

Commentary

Specialization at T = 7258/7029 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-28 10:41:19 UTC · history