curve #4037

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y² = x³ − x² − 16843953923963244361187712028580585x + 842558607820573175329602220794682444993704256234281

a-invariants

[0, -1, 0, -16843953923963244361187712028580585, 842558607820573175329602220794682444993704256234281]

c-invariants

[808509788350235729337010177371868096, -727970637156975218633717588665191256452499413155210240]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

233759478745101640748824952392657776103231094567203892525763394862296766938329605136863045952

discriminant (Δ)

-826411508433378236525114214034232450473350149460156595910161028757691683945826272801129996731096690688

Faltings height

18.4548

naive height

248.0442

primes of bad reduction

2, 3, 13, 17, 29, 1055437, 359326973, 500905264352731525025417650969814937290482225110302754911695498928574359

regulator

57495586822515554379715697.356032909468870415823837728310818877833613987182334178392198

submitted by

7fff-zip

submitted at

2026-10-06 18:45:40 UTC

later contributions

primes of bad reduction recorded · 7fff-zip · 2026-10-06 18:50:38 UTC

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

(4068256307675711971/49, 1388858404524387886796579144/343)
(69663013578037648, -2688517399034418938633467)
(-82361957218435675, -40879798711087821127365216)
(4154427384665089911473/22201, -215479761049578357324763044201408/3307949)
(124548457676130851, 26013562728948483504214464)
(-149884427824056703, -10807909463980173335880)
(303608820773667613/4, 9291551512576793049643625/8)
(430532269543878317995/4761, 2520133971723236132265514002256/328509)
(627493396000722775/9, 71919490573198214054219332/27)
(759240996904571029/9, -126527023528475642067828248/27)
(-144628401921758587, -15919368044996202868864848)
(215009107350246273, -84620287908252147876923592)
(61810298278363160, 6129913380054402148572009)
(31458434349407349/4, 213252743262400708314051867/8)
(1473581585691506981/25, 922869709785173712611020296/125)
(692137503086432173/9, 38363773211939376761384240/27)
(3879661237962192851, 7637490915318547968209053464)
(-3479172204841777381/25, 2770873342502408780250121128/125)
(-74463349790539178434592130455/548709081001, 10195396551841014209462204470660004538551416/406455703042409749)
(-158696659071465659387556093187/1428328546129, 62545013280588008455811759839824380556374760/1707034010349513383)
(-11853638129337730666560335/114768369, 47308186626685933447540168496378787752/1229513537097)
(-16256666663813236325871103511/157659025969, -2410783917994646571528904088179388416656928/62600565828329047)
(-6093834786799912554073859056/69626849161, -745463612300289246263734442286786925547847/18372367061263909)
(-50313549039569993384872617528594239107/2948736305491038025681, -5370679476632417736101112547255958093748457560179631431448/160123069001206029943587985455079)

Commentary

X1152, T = -265/619

last edited by 7fff-zip at 2026-10-06 18:45:40 UTC · history