curve #731

y² + xy = x³ − 1070854797641993070900044956832786933875468808447083060x + 432229579830395461350820542379167530001517819110289229471181420327211413782675600

a-invariants

[1, 0, 0, -1070854797641993070900044956832786933875468808447083060, 432229579830395461350820542379167530001517819110289229471181420327211413782675600]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

106643563452784474470296789904296550277566594367901089374451023650992563976483426820249802996476653889557765653772733314213601918070

naive height

384.8643

Faltings height

29.9492

discriminant (Δ)

-2116476529745725843401439784658969402045893066543736846266484102984031837679030752000308030452955539247733237479480952985925549831581450412866282655429888000000000

primes of bad reduction

2, 3, 5, 7, 13, 17, 23, 59, 89, 103, 31677151558182507977220975445000238418320926291, 343021196245559955052156434559301964512166292181342821018156848514504039

regulator

13161324422949178504623056300139292.6195273406576935434082301680384703375376250666551982463047713

submitted by

FNacc

submitted at

2026-09-15 01:27:47 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-15 06:30:25 UTC

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

(-902341519741804118102598808, -25764347773954772505163006841280550727668)
(-452819892556404126176073280, -28710365587518722837123671864675029542860)
(-1101603560387084973071126680, 16584861277755144212255557424950026288140)
(-332400089975537361099999880, -27412679271993572136518780938820545046260)
(-1152405494571662937689946520, -11655460342472163149855917185351424252660)
(-422476227518839844434756120, -28447040517894452196732058062897545740660)
(1664222436139016709590244470, 57090979132946109268401791671558898145890)
(-930783604192205557423182868, -24951387466597846484321433974974899873064)
(5349162102829395695616349480/9, 64587567171829301589978691632823351363780/27)
(508345933489863726321492680, -4385135282954295900885224179739129276020)
(643710187335898670852917010, 3104673323000179534628440653930661316600)
(-963667750265998252773921280, 23859220971590477055600208783075641969140)
(-1196539239818119445219211688, 675850642945021094465674619863175288732)
(-952798082644458168509945848, 24239736668083685381556687756259705677932)
(1762183243469931322247343080, 63381991306323909087974024323676372701580)
(-4768439218290587433234707485/4, 30639164649537957869937461670965899108975/8)
(-276647155492099821930789400, -26595219445361011925014518966278533869940)
(6231046217782006892541247339880/9409, -3353456559083233456064330699945042236847406580/912673)
(-27729658446471967728292480, -21491921629737118767034343407381483454860)
(5382391227626806912673949410, -388068386189094135719121556841812564001800)
(583421550452409593548228220, -2460742255182310571147861992703937137860)
(2410836657023653228134085055/4, -19191178327360671079410096210540906326255/8)
(1081729708479737246853680840, 23229903714147897526541250316003114317740)
(1820818334409195766830853220, 67224260058683716354779175068097999924640)
(1550785842582218146636118120, -50011048306184105223786816448505914223860)
(108016936770750338284668879080/121, 18234436649420043439602313482240613919149540/1331)
(720607618065058781515434410, -5895525431931783238571427815220576761800)
(5007882230158322589193633220, -347363807214451557447934004172491310055360)
(242009773792932829080555002684/25, 118401796879005209272271148895555551884877388/125)

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