curve #689

y² + xy = x³ − 2408214175466076412293618403036203976027332622020x + 1182661726073687627796398946489284803205462804121431349107158193549456400

a-invariants: [1, 0, 0, -2408214175466076412293618403036203976027332622020, 1182661726073687627796398946489284803205462804121431349107158193549456400]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 1533435676500539569759181614514630933450526096060095639730260404419899029551589883309296648669339297709517929377292010
naive height: 345.8225
Faltings height: 26.8213
discriminant (Δ): 289617804218546618532412409000237485186565522358253992235491299052454302008848551341661091631462607202628547194537356717845809329709111377920000000
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 29, 197, 31541, 6932371, 654795000413747519478975067107695513878454848715489090388643736265425448740399251223327917420159
regulator: 38002802850310549040341817008400.65003979207634851176396004555486713066774855259970722474176977
submitted by: FNacc
submitted at: 2026-09-10 01:02:38 UTC
last updated: 2026-09-10 01:02:38 UTC

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

(496169079654136926331272, 331555549594216370087266913172795516)
(563496729422933902806540, 67581223727947701740058018932558280)
(273505686400475031250440, -737876105102927946832041321280841220)
(555003665530064638149240, -130580601758802930553011642855065220)
(561684660303454471582920, 84914463777805551714649561968234300)
(541569144723782433413640, 193100790291582958444121322526403580)
(-1597508447259198265249590, 976170864705491030422788261360066510)
(555117224499146144212212, 129933748886818418378400358552430112)
(-1229285243280099949824760, 1511760250895279366907935604567369980)
(430997387948175754139880, -474119438733520342532557337337410820)
(-1665892566582090623731350, -755847887102059523048994097341088920)
(3568289041450469954590060/9, 14544578380745430671803313510153556760/27)
(420113358403971215355792, 495062406694726785924286453212494196)
(2023143621104661271527432, 2142766480864681300746798791018882556)
(1808201721223651700259720, -1655357737584375339314437655345273220)
(2265993802416597199806915/4, 116780785123678463291328454925937015/8)
(2284565814154913920096840/9, 20698900254016781191267254305324192660/27)
(26759049889539268541169160/9, 121668104886857113034609437111363693460/27)
(137611255213643797714293000, -1614185405745864607910786054969673372420)
(21229583939968028217205579560/2209, -3054725012639025418001179523854357572960060/103823)
(1169575352210192426856354690, 39998336420194541639897047295571658250280)
(5096355117665304260388280/9, 636322017962459364217676992592215060/27)
(15200803501678834924621245960/2209, -1829339678134937346575701533591707618016060/103823)
(131605795201727395457099110260/49729, -40510416814703226072053761702804923358254240/11089567)
(1209433712301870546898440, 197891824637121393559054247333238780)
(3270395720696776675619022, 5318395165260292378168935625545490266)
(1339131126350963545304476860/529, 40915029633318743509918868463082213937460/12167)
(14699102882022633826588205160/1849, 1749970504651554139263256434842500220117460/79507)

Commentary

No commentary yet.