curve #817

y² + xy = x³ − 4344574600050320996015196345051239966978216499087103535x + 3568190669047189407796609833147388404136600063442049966029159937823452187375703097

a-invariants

[1, 0, 0, -4344574600050320996015196345051239966978216499087103535, 3568190669047189407796609833147388404136600063442049966029159937823452187375703097]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

6289510257268917445359018712095790083232351068697190515988843833079422116444513885114607834217195318272318207206206883681946830

discriminant (Δ)

-251879924295090745194354714842111563559289591817126270372848421935824553071583343541424856953609366949586050651612849301340549343732371010751444613604579757568000000

Faltings height

30.3264

naive height

389.0860

primes of bad reduction

2, 3, 5, 7, 11, 13, 17, 37, 43, 47, 59, 71, 127, 33937948169981225001689780480045418727, 1303607454225626227371827484122976319075881743357459467818963887397077987

regulator

1441728187792338554184006010619785.14140935111582053228696196774512509371583497884041784330883174

submitted by

thomas

submitted at

2026-09-21 23:31:24 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-22 02:43:42 UTC

Witness: 29 independent points log in to add more points →

(1268027717032815101294129014, 9899706294668664722730391628328949946413)
(3376055283269463811275636934, 165469327358782595904998000609145062897533)
(2489597769726463414511853671446/1369, -2077110589180336376746341709299200376896296151/50653)
(-954705082504818390391873466, -82739355286710977999774806616580146809667)
(863493358691445484562160934, -21459681908918181747246768066442752606467)
(-173013662222967579771246296, 65686242757642187256442750926692296027603)
(4929667271928867927310423140694/841, 10333116007686216860034153191334938671221273137/24389)
(60735943115762601843071516934, -14959470940159995216418360586350064574214467)
(-312225004012438680221266106, -69958833661020796287273848260019532939587)
(9305768585680190109389936134, -876922623937120034881027717641800668028867)
(-996281547365354832307648016, 83112719260521168168349297742825263897333)
(7970618125979767401808062214, 689433549737475693840805478758476538263613)
(180727946824378132250053084, 52810109493555944065663835574307879672183)
(1577909657441223846169061734, 25328287725597283407271473013979263099933)
(-1447880910749871687962631566, -82603504337915279182812179568414794668967)
(-10258507717249730823075873051/16, -4994533084385331802017201644273917866860043/64)
(-927897823464470924645204666, -82465733378425322220689395340027234848067)
(-1482129630543138233106546566, 82168163184744525193930727325302651656033)
(3607400582051449387051371934, -186654483644457717303735522277341923919467)
(-136940385856501880202617966, -64502483621900854089560107015058404870667)
(-45363346330876497307660924601/100, -73794883913228932496900738911199441212082663/1000)
(-19008161301929595206848729689626/7921, 9321200520924967271028015588670859260274724197/704969)
(-47541162336020920539015203528757254/20133169, -2321882495753634957838586155685683014794377501410601/90337529303)
(56478101418341835729639244, -57645446452040161857739772043035601920537)
(3405326984986679049091437527446/2809, -1355883270428695860758800209181983773845081639/148877)
(680959621939313194012166734, 30421634718258799912490612857655597764933)
(932216051941243343746916939434/361, 670953512484596475002280099298434731298710167/6859)
(76188341747939583906295224790384/39601, -380459646646808310783288166664929634612435956883/7880599)
(655814154109751126367209434, -31638863888944446333870772321106548077467)

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