curve #1865

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y² + xy = x³ − 26622917338665208120324887402517325488x + 71627605505467803786363703677892796965146356590400168192

a-invariants

[1, 0, 0, -26622917338665208120324887402517325488, 71627605505467803786363703677892796965146356590400168192]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

41296218820607799358845338930420276650193591315238027219150109779075375899322370372115237550

discriminant (Δ)

-1008715809646754069221024545397440980477827653793650883102279875652445450991332323890196101986613866852207089920000

Faltings height

20.5809

naive height

270.7453

primes of bad reduction

2, 3, 5, 7, 17, 61, 113, 131, 223, 1913600709230170757347, 857705643255090922140918777224934359463605261992940087663

regulator

11969699233694065325441016.174905960294994730723834559237774241987501161133421955383864

submitted by

Ritik Jain

submitted at

2026-09-25 17:20:54 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:24:32 UTC

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

(19082645721031653819175471058/401882209, -2621353066361263548193906919707335465314818/8056532643823)
(61815471996947828368232/7921, 12982623363492291155528647489865416/704969)
(-35372309329945550464430848/6145441, -89058998727393873135356486645502913264/15234548239)
(257444355861599436472/9, 4069378591538681703357295050800/27)
(211521428831135488347166715493587890238140942622/72000850496246231787133987441, 83702539306023875557408521159783962343130421146482998423036768797643716/19319969644744897651422433125001340133525239)
(19354454629305690928/9, -133152427632207787476870077312/27)
(3295218001292187632, -4436246999438976270778524976)
(15724069978224281552, 59504002538420649338709535184)
(2794275176661969872, 4365028718031569770151823824)
(6412944646629066032, 12830984676625678559632040144)
(656645008976321577658448/97969, 427429830769723306048239208193469008/30664297)
(428037855292399893023408/97969, 190789568745355259762712489714041168/30664297)
(1771389764957479832, -5479630231204068427738665256)
(27060102232451080347532808/4765489, 105857978733029297641454796770396424688/10403062487)
(994988915582286705184688/97969, 893391862834560619834558701731674448/30664297)
(-5878419784324538608, 4999467823366701355444109264)
(176067602462469887696/25, 1909868095656728890739957378704/125)
(-11278721679188425922144403290293084/12075851440652041, 12980264988232031740701351710623662615667912657698016/1327017476390660662205339)
(-18301545550350061369778499728822/7973693955529, 247308232747360930815100432484040165260219587298/22515901701885990917)
(-5186044962037919633173568/4844401, 106037860228257942429827288938752413744/10662526601)
(-17426764169784606641370341775626473/5084010284644516, 4013955440591510468850517910665571461952816127759539/362501351982253302382936)
(435906813748029709487969792/184715281, 11759840173809333936713931190099698165104/2510465384071)
(25031933505801696944903/11236, 5758098531251157877367031821246237/1191016)
(-1046737014843115536965253910448/334825406881, 2160076180848777848441946086980605032768833744/193743708263028721)

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