curve #1679

y² + xy = x³ − 10181571439979503676087871183701440346715781213x + 392284142591581066170126001270728043131948029088233522547235516740017

a-invariants

[1, 0, 0, -10181571439979503676087871183701440346715781213, 392284142591581066170126001270728043131948029088233522547235516740017]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

328248525391764048542726027559396324028638137356539703743575146573567675110239559532323167484084701558076781782124350

discriminant (Δ)

1070735112972349331328288809737243876330972926253811702981216055013725188231474458417845617570263142290830639636079777323313176260935680000

Faltings height

25.3074

naive height

329.4243

primes of bad reduction

2, 3, 5, 29, 31, 37, 43, 47, 61, 797, 45965946398423827041928002819092510214907519, 7703142002076162314007096493350422366002708332505904011

regulator

8443260336099075462292236394091.9187353695532859404122246531118069436444742876729849289248461

submitted by

Ritik Jain

submitted at

2026-09-25 04:08:38 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 05:18:28 UTC

Witness: 27 independent points log in to add more points →

(9296288921349143881637179724249060593442353648178102443682/342181630311662230956736832091878401, -2331938076423419925376190344682102502671187145771686443217562368820415669192261698850351/200163569304233348902929263351542482183556208312996351)
(3781016268770619925165394/25, -6010219336272775433027068453330678157/125)
(-84012084971671122776930494/5041, -8449572058397589038368899355152712973831/357911)
(23253694857720377554635586/81, 105967778310349147884900662162210326231/729)
(251104604777407157228543/4, 5743119710525715789975947347274437/8)
(-606083589460830921114763/16, 1721599509043871481493275062056883741/64)
(4168117590130525355552614978/289, -269091105792915730377058159888949428188193/4913)
(-32101232225153458332603276178/303601, -2832632002408450876275245163636032925172751/167284151)
(87799291143433643808587168/361, -760773711830181418868213956386953642227/6859)
(166360943812417410353354338/2209, -753281971798570319389655785983982048063/103823)
(3856981856839694769016832, -7572237200937752589767935084679809351)
(65392531196874048894626, -2473025215390776276479874601243345)
(2225588286707182833604756738/33489, -18546012769398891007855124135537018956247/6128487)
(-224957743943352492523652923/1936, -216921311213717167864768252839388053359/85184)
(5526127390431374102281354/25, 11820379385033367599259285564358375523/125)
(1453516058844355261484353330182669512162/1635174341669521, -55072695362555765317750901392228776801490091116756869276649/66122017419475163168569)
(1914272692964379892433318122898098418/24773923430281, -1008597199940751589523983454583411650667536167444566773/123308264820398262821)
(7901616991957391947607482/121, 3227351243522914306539422343669325709/1331)
(41906031785713396559920745249140318172815414629917648/593275090927826282954972506681, 2308862469308203227398943424536873183166308830372974032410842340652255446342875/456966298533834007905781269392867401693501421)
(12359033713651482979271348/529, 157309571157153789188534153148971487193/12167)
(199713474396943660609266492067809218/6681723519409, 184947139960403719531142826477353269237658841509650553/17271607170490882327)
(6019895101779811455056708181051539116014227/149221528393239465604, 12522601446377362985149470871462915124461526729127175657282083395/1822834441987248654340593276808)
(1752397135270390129511117974506160431725098546/47683482563457388207561, 85699278132154551850491160387546448725545073479187869297703998698005/10412426526140753200537404683421691)
(2927498158933384138028773702020184985326583093/177853880109834201425296, 1135425210525123416344886038574059522508266326158442336276211256624923/75005829176978376917755742667057344)
(1501491987506495963219109890113456700739155834774798/34605175170735832791003221641, 36528719023717970338495330897176992326457612149543017038342472480538096134157/6437416042353114593153371839028156293310811)
(1302703520905100312835957508/7569, 40261313472139190497397292677286049554347/658503)
(1427507029970568559082842991426/22193521, 195694387912085373312163802339167149348222809/104553677431)

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