curve #1391

y² + xy = x³ − 159400488349911348382958265607695692564740378638910x + 759264644720519887178037336876808132547450704568946150299609844790213883972

a-invariants

[1, 0, 0, -159400488349911348382958265607695692564740378638910, 759264644720519887178037336876808132547450704568946150299609844790213883972]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

32550251860759865410330536277649720340610304368193845320577383852031746893262417224836653716473314647162139071496384510

discriminant (Δ)

10167737839853297817955150523942874777633966456660252921476492770171820870414709130149338125310768592265062981353505968535268999061871437255449920000000

Faltings height

27.7624

naive height

358.4001

primes of bad reduction

2, 3, 5, 7, 11, 13, 23, 29, 53, 83, 167, 197, 13679, 3467353, 72959366437, 3244913067087423859131732841449963161807036557409793810477823115106394744007871629

regulator

29981061627880582584228520365256.92009027540163634726340962599320508446504819261594371111747714

submitted by

Ritik Jain

submitted at

2026-09-24 21:25:17 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 04:51:07 UTC

Witness: 28 independent points log in to add more points →

(-37618104052974426454555993561107136531231558878797125311604/22841839726447113762345370672720369, -110109313657949968836045802005294861535248530751570876790618812868961729434372644533801326/3452205338898770505126180869762703329993979230830153)
(331760765025811866040300389596/97969, 492834426822431335402061801095024899619309826/30664297)
(6348258483216870093844346744/121, 492307723484286217264268652015075811336438/1331)
(482437236993675654575387324, 10592877087919920630860589286643999996498)
(93524772863488800426707656/9, 404987324502394976882447692073051135266/27)
(33077849217411422978144, -27458915776003147505848686599825877682)
(34293659943881646034713069044/3481, -2473613357078763047027541758489554460496458/205379)
(269340278136039810306787658/49, 2404939045694481394065643107477183545210/343)
(13812209928509357223967412, -34534701201991398134345720580469040710)
(29456087007070596883585724, 147043700031658805109818409330874978898)
(434500267608072550674094684/81, 5578703963110519153967935396395642121442/729)
(2946499325796861505558833406/9, 159823651302269541994701742479469294197266/27)
(-450492901384543635678011584/49, -13050473617025546042512060356764532665506/343)
(-11093457196822576297366468, -34093300375375091369810261954621520142)
(-1379048479350090634923676, 31248408059731420799731495352636548178)
(6363862400957020562010284, -1609443578802328174528871587189454542)
(419164918390514707156673935405338132418396/133173607967569, 271377540925412895203601997312995777651091018511220112089878174/1536835022049639438503)
(6310064698910902442591010438524/516961, 9345539792602810641085246669297241164155485422/371694959)
(-505760834710663575228304450533759343376852211312676/842550114606541700975220361, 715004328667218921593280794951683122764987715846330997626019066066315508365978/24456461047250778255860795028113356223141)
(-456639883382936457931426480687525398700330435708/34492394570265723494209, 150124831532707338860511459343439886354527348068787677203206459647551122/6405971737218446703199526051710177)
(174081327641965536553777786019607604162488124766092/17453765906130405007559209, 926958124150019023141101280319526929264012562720641835096989669307372017818/72917827387944667689777202746361903573)
(17530510874738638894150819914697555469313959/2749507605487733476, 6666036682283574844634404583244838699595963756082820535264551483/4559134325682399285405786776)
(879768793305192816760190640962696722882436/146095168593696529, 235231335684856698250855816234442690608692783061465798606908314/55841076360368184445475833)
(-1993773555783881155364198298629211124/143302373809, 913906048817840267440135998916624025309188640021707346/54247543512518377)
(-176697686621272978890867016803004/15499969, 2019233383231692269723493476754686032479755263274/61023377953)
(628976913532015866263615972433160971792236/72640888632549169, 104030247908137394147147841832370900000676826528941245797969154/19578153199690941668448553)
(202044431618689950264220962629159108/20383558441, 36012935625901212471985307033523290788237956387009326/2910181022180011)
(-14289975386137547809132882485341864836/1002823990921, 11762913920035336856376768557355604440878874147928662598/1004238975572189531)

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