curve #6144

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y² = x³ + x² − 918351646583012106811183254174363220540x + 10715279791010518395972883673980792668750168584782458112400

a-invariants

[0, 1, 0, -918351646583012106811183254174363220540, 10715279791010518395972883673980792668750168584782458112400]

c-invariants

[44080879035984581126936796200369434585936, -9258001739433087894385056768535312352561766434454260416629184]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

4901472636772735736465174113450594347847928376352827212330901920368892490934682792721772656206969474280

discriminant (Δ)

-32399751184639913560700117413536969637601985012830281085153820355786855910270122206570407025354231171156713100000000

Faltings height

21.1309

naive height

280.7612

primes of bad reduction

2, 3, 5, 13, 31, 576293, 13591531, 238933789, 640084547, 84608433276950436036624067501592632724533586162543432167369587378257

regulator

36202249596885347872621861882.9799926878190139045276181136795746234456348242691033787922737

submitted by

Ritik Jain

submitted at

2026-10-29 13:47:56 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:55:59 UTC

Witness: 26 independent points log in to add more points →

(50295124924126494012754848783022334537221726492179980/3242710286257433217426997329757849, 2628933632098171495417096536988474854795718961877995285470515482337429684116700/184655489825486738747881285301339931608881451341507)
(20925450902221732535, 25711451837140573228688967510)
(15077009511316294818194/841, -89088723834587174468924284303710/24389)
(8244650875170649765630/529, -166904485158763916190787899325650/12167)
(19045392142130574035, -11540787944311741173805927260)
(41884959421692459220670/2401, -224422989608825999075390989673250/117649)
(91919270563550361920, 838415757663564662487719032500)
(17951149664690755930, -3802388600980672650155443890)
(2367782707591815777470/121, -20524855406865264418317039023850/1331)
(26303923036334657120, 68982733697317237499862188700)
(14419380466203287360, 21708856047420273217754523060)
(17865014527500252170, -3269538622057160576393214750)
(862348948587253203155/49, -690741247396267523713234662600/343)
(-2189115010975939220500/121, -194745927480408833521203395310420/1331)
(-3974209220635597210, -119591936873852840501707630170)
(-9378813565444333610148305/724201, -88103083351919635245225817334704367850/616295051)
(262550934878498077540880005280/26350704241, 216181789045452454559092284632021203076338140/4277483468737289)
(315273496912253273872256/1225, -175848166242544402290674045269359396/42875)
(30457849799498384103020/1681, -338297497213965664098453022975500/68921)
(2125003754167102022240/121, 2569837492887611640756672137580/1331)
(7843367253544630005830/361, 218913467232013013902827333741390/6859)
(45398087686819174570, -250177359007287584493899380350)
(1074969306055716970775, 35230866884278687106426820994830)
(3759535273502070539518873361652902651552183/221039120917534074137761, 414004782345652077534730189892379473629284676743648016832864286/103921095687764670129277057947312241)
(9294663731288523890023464877731539392861143680/884596304515098966472578961, -1241299203815044045336161592132455166314701851747668991533533087504460/26309808141284366246714460533288069061959)
(998777985647765359269029425226370352472252224440738179677788551579907514306723432718/47249792609087653480926432774533674358342789246400110411799012601, 280907773618521591763512266767116447193277309705539318935478410649242200860111573793700276685504755884370575994798906918869094/10270695647889463290919121291748789975543425845020752022386057040512933833772638427222037963102349)

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