curve #540

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y² + xy = x³ − 4499601412550702202690748804041515406730x + 258062416605292927548451609701680383529182599228300373796900

a-invariants: [1, 0, 0, -4499601412550702202690748804041515406730, 258062416605292927548451609701680383529182599228300373796900]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 4530145033569689985755898776442684357079418014436761267732395368513844579990782108338095146616502758114930
discriminant (Δ): -22939112664060301006433871229920898102210231901644260064016399116900305246020042197833987721834246623838510891215744000000
Faltings height: 21.9754
naive height: 287.1242
primes of bad reduction: 2, 3, 5, 13, 19, 893700887950885410762325874064513059205939803, 684071833554820758363947307074002142798720507216415119891
regulator: 15742890605075582142114658091.95668229684638016872291555407708936772984707981508507071925
submitted by: wgxli
submitted at: 2026-09-02 22:39:16 UTC
last updated: 2026-09-02 22:39:16 UTC

Witness: 25 independent points log in to add more points →

(4961129830280494094385788746721164584481835/201244472358221705956, 11050178275727213717240514205318060556388550971675961516044441905/2854867393975668059326117694104)
(4341763900178893320410, 286054083564646948672286699559770)
(8617087632063250940178260/10201, 25220905985537717408891279370815070670/1030301)
(1459561362746537470115/4, 54961520445860356081361598683335/8)
(63078705510280960576531035020/126315121, -15715495079225775602793212334624328617782710/1419655644919)
(299821588081380243910, -5085355661201183234932513656230)
(24383949315444662265860, -3807627291031565648484411812509930)
(133396596056959246912052767901756/1274832937225, 1390294502946352564500523650849571533790744614166/1439394746926689125)
(1145656628283710867089338801116660/88069009171081, -371210362709905210461846021339336129408149324659970/826484409187092184229)
(6400600965197804103688920350180/86881689049, 14630943607337340014474746308308359556609085710/25608986019016093)
(-11696352018487334041591554497897290/143519896840441, 496811512777088761754230580785799220986625203944430/1719365350230649530739)
(2551162978494468381797060/11881, 3926383012516779295473744744899512430/1295029)
(588686888161259230728343463493758960/11826771083419681, 510299710309883461045667215527787446534530477064610330/1286172697195359308224079)
(-3240361596911730185190340/78961, -13562040119041871425246325382305029130/22188041)
(27307520845186585460, -394401691823038947584789525530)
(-70427812332165167956976168870365/1086860460676, 596934775563765135811745195935425575625394804945/1133080288626707576)
(1167153799912370768140/9, 36778941594261155161731829253690/27)
(452523624284453265791203488792062131250776340/4680233823946835960521, -9626352942183337230342094586983773824578602843338836197311863670210/320185253696153538130268791714181)
(163479427941196231777514734586232696941366425748/344013963360868305100707409, -65517368187601729190497415538519195942012645953731512555428113489394666/6380638001487979634767538210737992559577)
(2836177854092844299930947094378606979403010/10054865564612253320329, -4667554945642876860564465313920613748208152554174801817524989020/1008241112753819956577331922756517)
(29973157004853037838420161749702368/36564310266649, 5172996559417788424512608615202757165460700897140882/221098643585714639107)
(30593470686517148183012725355/130279396, -5183480208185330415766220882337375542377295/1487009025944)
(19581620256320068783874991508896299060/40733936505903001, -85904711713574324694282985272665807904787146650182902130/8221187876942568537229501)
(720699399492813386428942176958529091860/13888232524978993801, -20979580874632109284302574393503235745597012888925787892930/51757163670043996393315905701)
(-572603482155255262369499320/55160329, -225750626166278294154053735797544529191870/409675763483)

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