{
  "id": 4023,
  "curve_key": "-568621141031031703329608942242958629075679:-8610978015338861696951775303488449880319262993705721785889147185",
  "ainvs": [
    "1",
    "0",
    "0",
    "11846273771479827152700186296728304772410",
    "9966409739975534371472949346296292161891501628610053499806436"
  ],
  "rank_lower_bound": 18,
  "torsion": [
    2
  ],
  "naive_height": 294.43179752249057,
  "faltings_height": 22.594163108852108,
  "conductor": "100333804916069595557644850229910002358198035153406924766836550463004943183082",
  "bad_primes": [
    "2",
    "3",
    "11",
    "23",
    "73",
    "83",
    "89",
    "127",
    "157",
    "197",
    "199",
    "353",
    "541",
    "563",
    "757",
    "853",
    "4703",
    "6449",
    "25471",
    "29833",
    "190711",
    "203857",
    "304063",
    "437153",
    "18963911"
  ],
  "discriminant": "-43016663573687271933898947634670450188852045984282007227924321986240777342507467612061512245823300597964579994697753108873088",
  "regulator": "469480277139169630485089262.57452701837558326828543447518430548866081563024",
  "points": [
    [
      "709957347969041571956",
      "19396475454182669928178486277786"
    ],
    [
      "911413394681994953636",
      "27889980552479929103724191842106"
    ],
    [
      "13085667497197703851946",
      "1496958666917335151005789925421608"
    ],
    [
      "84044732244206789212079716/3721",
      "770497044188261356042439650307366786698/226981"
    ],
    [
      "68101636646026679519/4",
      "25516153265702077696990725503689/8"
    ],
    [
      "141464585011100198306",
      "3804373744328455191324615495758"
    ],
    [
      "782614938522471112607/4",
      "35574262617501871275852547710289/8"
    ],
    [
      "750039709135591143728",
      "20995085095620287313352764143594"
    ],
    [
      "-5288866552998774961629596576/105206049",
      "3280855450590078302530888576151045271004438/1079098444593"
    ],
    [
      "-1112994392247678175817836588/6880129",
      "35256226267418412329366056344208535085998/18046578367"
    ],
    [
      "651583014426545916499892/529",
      "529407020132723487370313990916292918/12167"
    ],
    [
      "12948205047013709319523024/42025",
      "56404377153965886341904835761483780658/8615125"
    ],
    [
      "-802361720654205488598908/8649",
      "2284862836394006096742829461590016106/804357"
    ],
    [
      "-601746800477551743637381324/11122225",
      "112306274744830249697855212263679030185046/37092620375"
    ],
    [
      "248669433198046109929320418436/899940001",
      "158198257799821373574474383459951615303544742/26997300089999"
    ],
    [
      "3369064646260046695257463886584/2943388009",
      "6232239372088036952062026598158789963778540882/159687629652277"
    ],
    [
      "40153717531302495944949762694/176703849",
      "11600961264821800354917419613011412595380556/2348924264757"
    ],
    [
      "872283619367036423476942716349972/3295905904369",
      "33656859888544038077203375261954891322059791024286/5983595220863457847"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3723 (source contributor: Matej Jurasić). Source equation and witness provenance are credited to that entry. Exact rank 18: 18 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:47:58",
  "updated_at": "2026-10-05 04:47:58"
}