curve #5988

y² + xy = x³ − 95235294399152131786921756424389048251441078650089749971097466040x + 11659293871962868377403899260228801541614449806777126773289485956144428280106713688192049468609600

a-invariants

[1, 0, 0, -95235294399152131786921756424389048251441078650089749971097466040, 11659293871962868377403899260228801541614449806777126773289485956144428280106713688192049468609600]

c-invariants

[4571294131159302325772244308370674316069171775204307998612678369921, -10073629905375918278076968960837691388896081372008926190488578422120260137769863433059928659896249281]

rank (lower bound)

≥ 31

torsion subgroup

trivial

conductor (N)

12804656153078547918527945568389057641211676647902065476729849355220176499948959941047199085232555969506562742702529141868356238331317105343669789099167170755724113926410

discriminant (Δ)

-3444976914119439637619599741484775724953557368148415526338521559938570878854871944547378341961318600905064255525719930583426813870804262772301491589408342116893810735224432781969343391597824000000

Faltings height

36.2918

naive height

460.5317

primes of bad reduction

2, 3, 5, 7, 11, 17, 19, 29, 71, 6537523, 9103769480736485747, 2366213327227514390407301768138355738715333, 59184596855962307780015721941907124794945090139016919178434167608927069460030367671081084051

regulator

95580918118341313868893623706272136634128.18227453116988400959483373291298071106778184404929421882812

submitted by

FNacc

submitted at

2026-10-27 16:09:54 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-27 17:54:23 UTC

Witness: 31 independent points log in to add more points →

(-1976165991808755303106290061145224670/19881, -12581296968984611496273278056376508736290190090789320140/2803221)
(-341119644713198072483738618212820, -2110059429272193883692225256012813744910995484840)
(22197842277786714385884330086646423223029819965924195171534118074647886564273192080/111629448784461910375280903049167972088290742873481, -901786023966257542362740606038857170300764113425154878718917652829198482072985599756624246692706778403350385208964633683640/1179419137259299397107615617335091425880110648103171671968111900440843299621)
(-973905430627326141502868835561026636/4225, 1269345586036509940932746728536898273880436883249740632/274625)
(-24338668388775663344780694999188720/121, 6338297240517188878550029191277355826872547240527960/1331)
(63573845997343663179840288575680, 2421107627333225041958045771208503045985346407160)
(-3280758215019140890351918003063175575040/10843849, -127651635973759310708305997972046649857017136250417024683880/35708794757)
(6387875194759734044160542571907120/289, -15194655928436753995457508627839321593564168078652920/4913)
(63687672626254617764833919317600, -2419153661894928779523166820564623517004046387640)
(10509396859317405596933584309177504/49, -359669269631148813006972872922552736225360723240664/343)
(231669243266586380095609009839927670/1369, -31600857356256305546602259611071036113717895633414770/50653)
(380212805608920802367728860834297520/1369, 130445505864037803077140458756324267912664278859626280/50653)
(420225468481788448811098136542000, 6770995469833678836003978451008236003277732213640)
(13884180520350613026607167287609320/169, -4603092647883862117059992708003205062376376218458480/2197)
(220526132323920857579398231670800, -1175584958439555950747622948766306850385718339160)
(-7577929248840270655220826709664607920/25921, 15899640104101091961278204667603723608021357339547277160/4173281)
(919779390748574008815109993925018275/1156, 824064514411602769000198163504148625789667462759100835/39304)
(253114991161644271014065652189093062320/1026169, 1852441550634068137774840599962654715924008866363721073320/1039509197)
(739816870343251496347426411919284984/4225, 162967820314693756860217265165959617829784969457961472/274625)
(2283316733952316715890071842816560, 108158954152118462046015136364074838334165764204680)
(31775837664244379599906706910375155935720/251444449, 5109642194259810009659333316617709214027313993628674863396880/3987154627793)
(20010835718075550312415421785474717748296/90231001, 1030743236581881653995546082687862703729810325252948864314648/857104278499)
(561478790245901413768546621960600, 11627451093846887016516876933170990943608672452360)
(2446335749642617216783986314962480, 120078813441491891868176308328713277275793510913160)
(594630330208704009476288512773629230/121, 457650565567911364960956940804576834081398050307154460/1331)
(461758739759520664306066828232838040/1849, 147699300609997541153712547843217248759261539302951320/79507)
(87269820817541268335613696908462254/625, 16266729721352749777174747544830432238952165491026708/15625)
(4994528035287306269380499149175285833900/10439361, 293287579222926666889114431763245194972191414279120153662340/33729575391)
(22968979866586112493663807688344684220/5329, 109806565909525561963905531659330529089600111869956253720/389017)
(87360925907743593140350954928387062320/4489, 816434928167719149747243917353880639549852028304875555480/300763)
(65284637534496754976931253856247611560/619369, 814495168334166499002901544984548274873593043025687355480/487443403)

Commentary

No commentary yet.