curve #807

y² + xy = x³ − 28204848322062881530889393633941517015722940860x + 1807540682554400161478666961448450111233752757159879808835808783840272

a-invariants: [1, 0, 0, -28204848322062881530889393633941517015722940860, 1807540682554400161478666961448450111233752757159879808835808783840272]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 246523882880166447225036467389825414647399566178502564620132267874049737720973849182238010713116329490772127390
discriminant (Δ): 24557716723221241923593099220358794559395373547580115314398653293744584688136157891240489607719272812250812857399906776305107222307840000000
Faltings height: 25.5654
naive height: 332.4811
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 43, 59, 229, 37480585581630899238799480222795161506518713103673469791601070693168077287570256779578069762648453
regulator: 22093845273604088036442487152444977.2607873752994286557427434453742743444087128646846133251
submitted by: hdeping
submitted at: 2026-09-20 16:26:46 UTC
last updated: 2026-09-20 16:26:46 UTC

Witness: 26 independent points log in to add more points →

(-774693953708396088584989/4, 18747679059526606535063820390140239/8)
(-54894702826435867448939464/289, 86739124938537040833594224273621151364/4913)
(-164986855330461000901726, 44383762995617205795873779918974928)
(-121912041579482692838416, -58601433535168617866379114704746492)
(1345616475263180051570132861/21904, 56772138399389152524872037941962572758411/3241792)
(124044937944534287250104, 14750243100617697366157745170065668)
(258747315813720988481384, 108778626380970809440653698149304708)
(89471818040232211070024, -491914857723999486613072071221452)
(940814493023812166042488/9, -32621326539843059402028079292101780/27)
(104844439420996992321034, -1704882422112143400623616636671642)
(82277781722251906583534, -6625612813864471857212548802915392)
(150287224290299374472624, -31034450277147264053827140230094772)
(595537980925901317689584, 442975450932367933062497206347312908)
(-139017178505511650058269/4, -419203201067374268749605604998435541/8)
(3079613235867565862564056/9, -4846559767616747074456737342563044084/27)
(-156099910768951073570216, -49057109890452698915507557913932892)
(-127074232611017104240216, 57789905223547397031786477573983108)
(-1337006054799623003938165547251407085218224050312385589674848/356325200047156934868433343831925608929, 294214056982623186164885644041294991450977896572564759950323929299696142180433278467591071428/6726200460909299598311888844963955402425067122175876478033)
(-252328642869603317512112396667643917235424895105427274216894522536/3214892998826829207224384537264420370332521, -342857860061099956034316362232906065146277586855969449419123188940760849833985723077827847185525548/5764342592249642612927910134791263270751710193004230083130454069)
(-2598587859685906420219851395566501965794284247852469998183104/18802643256847828658183520318120381769, 4514431087505782859566705678122725540769059381209944530655127069387149653444512782451630124/81532049478565538352243632360438728872772581775663542853)
(-2760618204603339665730104324570750236023670984391458790905750629352/18567128406351006206326189070381209102527649, -4168127960850071360410639394514351691995486715101853267141429926484861095016821459755576443531293124/80004996650769176989250441683305832911760538788565150236992798607)
(-306060513109007293550613964006629076573149281079367974981835936/7052518489742955296245382966578323049321, -32167287434057005487896804649345092466632167623817049884821729756301490117393893915161089197652/592265383823284779743283881135681297077634752382631666653131)
(-3641000616530036804638482000713877026591736350781536533006345216/46624609466812599745776899432187140777041, 598478609809553498337469377579281063620646364629659640054967952695331618624715745758936821409308/10067527178143281150536930382148480411449336051038144401107161)
(-442294251527964627923191290495077530494327460879121918944/5971641960333117275616065152081369, -27262699078852212710684616281489547444851182550985372897507669812065666169102741600756/461466991368289290266175615485172181038567292834403)
(-5582065210716408624868594933145575294272111923656334888593024/28813107144367341306536798165389882369, 100952947929888944193328081963617944931021752528450106412198632281784876240774602307118084/154662541085438284452414509629011702300017600545332539903)
(-10827364594341992149893649151203057586507749990241611717950956704/482526461593704746942273390208222590199025, 16519882098247134741913302034232073371791666298827089029837134631615220745082209328323286193824516/335182782839124034306031481980613123170976138865596599672536375)

Commentary

Fiber T = -683/2288 of the wgxli #302 elliptic K3 fibration (Gonzalez-Rotger 2004 / Elkies 2007), with 26 independent rational points.

last edited by hdeping at 2026-09-27 08:22:50 UTC · history