curve #6137

y² + xy + y = x³ − x² − 4898895797272237789438125198133520612510697x + 4153070427678981369709255973846413359090415617703998185441703465

a-invariants

[1, -1, 1, -4898895797272237789438125198133520612510697, 4153070427678981369709255973846413359090415617703998185441703465]

c-invariants

[235146998269067413893030009510408989400513441, -3588252849514639903427738999911090338891600458653457591769329483505]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

29267677796440548091196367462585711496240653050366889498086152167855540941216482176204102099067491754771786

discriminant (Δ)

73313462581280845716238564376239272896401141259935895447529700370582839024287822076269012286434784596902979743309409512617541632

Faltings height

23.3771

naive height

306.5064

primes of bad reduction

2, 11, 13, 17, 23, 29, 41, 59, 109, 668869, 17497699, 4569204612716749, 908907438614130168428561, 704211051935751212762195566383660166624381

regulator

230914851037753774258525462906.86792776081686574792739921005701600642957937964471599753950470

submitted by

Ritik Jain

submitted at

2026-10-29 13:47:25 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:55:30 UTC

Witness: 27 independent points log in to add more points →

(53499021471863345891902545/11881, -350843970042554899215218104179985230784/1295029)
(506213165716496726171710443612767/366086712601, 1061181413470488649986242543569336274777274079252/221501131545947651)
(1531555253326313608679, 15577259627176099301499428269820)
(177522884206440222314501/1369, 3005219241323952075132722248960961930/50653)
(7461281590574317263615, 618850523030748841658811782614460)
(426545060771392418625055/361, 25923407468419715442145801935665076/6859)
(4217736946347961219058655/6889, -21265961806280756955217718337820696652/571787)
(4075062547023162236782851/961, -7274638827281491816599741596043192028/29791)
(3045494275124465055426535/3249, -3632044488097482003966404576252620820/185193)
(20639683934887514274569519/1369, -92809430129366004471733901908991591764/50653)
(1924512079572032448067439/1369, 337620560958616699453820729362419116/50653)
(511176468670765896713, 42218968383820095981842358778934)
(30934155126853559630621/16, -2795977248160077767767996435398581/64)
(1183876508909621613610719/361, -1048256633836341618592723233209297740/6859)
(1083712970428711787889439/225, -1025322994673348790176862458589741692/3375)
(2399421237411986389481451/1369, -1561983035109351175987814257159986880/50653)
(24951485558707386759466788112069286116105745547424560673533/59057654022206094423316803380291281, -3941292472859486457833025625563610640780227004001251367078065851489975586119778851760738/14352061506665527469535194102779567195135562651508071)
(13988830416298181353371, -1634949776356574712467275261338948)
(116697351250738115117975/49, 26555555884114837613561393237169412/343)
(3847850362188863178775, -205606278608409644057811071337716)
(1352047136480146983591, 1056926182254760462669259365916)
(90666213790966232312135, 27292290423629407902303848395388444)
(1063454342055461451674943/961, 277934869275481752133520931481167932/29791)
(-10928280529154814638241/25, 9851238878974778826717906003328492/125)
(-35254696735139784072481/169, 157908214084720507162426739610370892/2197)
(48972216993942749129311/9, 10052058891871834991689890992319220/27)
(89520044217613761097641691/441, 846944051952271594808938018183397040496/9261)

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