{
  "id": 456,
  "curve_key": "57883617690433150658066967442889281:-12479361728688027800444520801089064569912838458264929",
  "ainvs": [
    "1",
    "0",
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    "14443705704500032075948025770184419656032855664272"
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  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 240.13122741571104,
  "faltings_height": 17.986681684546006,
  "conductor": "146613446594376348938349836157250876838301559148938669816385485863579137947530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "61",
    "617",
    "6011",
    "543210295115966222910879889041768196379364320359872798404383979"
  ],
  "discriminant": "22109580904243323101474980159758459092807147453162165592143262171871673898004061991715263307929600000",
  "regulator": "163465550950442862357.987581461528240530403905584604104104506858511252338502823",
  "points": [
    [
      "-19976854285990312",
      "5528264733209596358404916"
    ],
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      "-7877865701744476",
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      "28587157664390174",
      "1825475297199891173214128"
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      "8635554351354584",
      "2161941952608761389209908"
    ],
    [
      "79513143295218104",
      "20524795628597673805310228"
    ],
    [
      "45648809845665731/4",
      "11779135511012382369549079/8"
    ],
    [
      "285021874077368216/25",
      "184440730545424867907605924/125"
    ],
    [
      "4871940471466904",
      "2946901712725322736870068"
    ],
    [
      "26271836211361394",
      "-946222783374548104501312"
    ],
    [
      "118798799412958864",
      "-39342204356988588490211012"
    ],
    [
      "297935023591385656/9",
      "-88734826172816658752695684/27"
    ],
    [
      "1196033328913219124/121",
      "2486364711370641475537091308/1331"
    ],
    [
      "60392255234864024",
      "-12723217863409701291434572"
    ],
    [
      "-26695329967193416",
      "5254679767990263723801908"
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  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -28. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 20.",
  "created_at": "2026-08-30 15:55:18",
  "updated_at": "2026-08-30 15:55:18"
}