curve #6151

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y² + xy = x³ − 29389844791300802474167961053828738x + 1964872730089836947175948981179506773032538226295492

a-invariants

[1, 0, 0, -29389844791300802474167961053828738, 1964872730089836947175948981179506773032538226295492]

c-invariants

[1410712549982438518760062130583779425, -1697650038797619124476088744712751630040206223394974225]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

233158497597091061231434614363200136120640794107364705251101906262838259712114321035950

discriminant (Δ)

-43138104352018949442700632403921277128284601519840328113116730924760081137757662024752212645666488320000

Faltings height

18.6880

naive height

249.7377

primes of bad reduction

2, 3, 5, 7, 23, 83, 689893, 177793927699, 135475049430625804230329023363831135673651819250097937096722879

regulator

3605760382020715235627897.9945402875492137010733210975774564986408746752067509933887486

submitted by

Ritik Jain

submitted at

2026-10-29 13:48:26 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:56:13 UTC

Witness: 24 independent points log in to add more points →

(87648863503521463632191828/1448030809, -1112575434104464957548697476073639491082/55101916374877)
(-29739082091024092732/169, -90252533313181668463821577402/2197)
(124677963512933710992801865754806480142/3603745229292978941161, 6805132927361632706393771314738682650357481520815018337344/216337158288313761035962346814091)
(8683633869844178758244/27889, 706338280266971887436665463070562/4657463)
(124009201192905956, 15076803924866331750117230)
(-17043712664264713372/169, 137257490219431779170524273958/2197)
(738961203883712804/289, -213573756099203508943593029810/4913)
(80263920270234692, -11091103480099119326167666)
(53764796494030313912/961, 663291486792619933999151325734/29791)
(76051827461161892, 13022903007196898797875374)
(10758645808464155012/121, -9837611637042554592594044246/1331)
(106028279847632036, -6378679644148412488675666)
(255840067447763873252/961, 3397878270356827127650608807314/29791)
(11073461399372531696/121, -8594345733917040825020909786/1331)
(-30697246212121372, -53274134180700384920902738)
(73925237480543012, 14007801937063267382368814)
(5706809341220620901858/52441, -89315478719056293081329905066342/12008989)
(44161873946304589517853491/188356, -293475009008068260392483118721018037105/81746504)
(3268620087398656100558123/12096484, 4933842507075342377925115289448937793/42071571352)
(166899751167533252, 41337579217470306573995054)
(257584289691707396207012/1437601, 85339284886762814460377975023448626/1723683599)
(399695838563536292, 232533841574531613559343534)
(192813629524769259401/1600, 842292755975301801050304663929/64000)
(11399701669841955203964428/3751969, 38429351851687661807481344055422871022/7267563953)

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