{
  "id": 630,
  "curve_key": "22948068435119922764790897395244506803917543869776:-102939319767546694810541697722055776111594257530729862334531421989096866240",
  "ainvs": [
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    "1",
    "0",
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    "119142731212438304178867546335237459944511190723779503318854859356288944"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 340.97195469789506,
  "faltings_height": 26.36560692735078,
  "conductor": "625847273392133749141084531784604199332000011136824937628804232804540038348472590036929315025313329802578398367238396088",
  "bad_primes": [
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    "3",
    "7",
    "11",
    "13",
    "23",
    "37",
    "1223",
    "24437972051",
    "561063059024179810500844410439",
    "1825535106347063733958801675489652807861250517266415081493807015950621"
  ],
  "discriminant": "861265623558584942823941824946868543987257828061527080055139637101120161140597943176655121328773583392980179877870893149948554653730382857870592",
  "regulator": "24236510207521892374816692833903.861518567390024375340731991595394554991956747072736883155144",
  "points": [
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      "17433140163317800903227686/25",
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      "1157968384363419683673312958/5041",
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      "13314547971206989228789570/81",
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      "-7986443927573349154539106/25",
      "61143901852462354572971542193470372878/125"
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      "-3642222329410685466032117722/9409",
      "-452858549349607077540383669747675126667618/912673"
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      "433102838826316746957623402/1681",
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      "-128074317074627888032189",
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    ],
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      "1501660173050891496579349193/3136",
      "-554483402212345171121593714008446040795/175616"
    ],
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      "4424868099066997549873823771194/26245129",
      "27988089409984321151212127980896182989794564942/134453795867"
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      "264854971289458866152756551081690062"
    ],
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      "64595182975169807860676360/121",
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      "-40258437569358328664876032138/208849",
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      "149148850212614015881816024530642438"
    ],
    [
      "644516148247215773856407825/1024",
      "8518215494606766190616647848620965751559/32768"
    ],
    [
      "83470981518157502874820424/529",
      "-2655481912630607309209690563065943819108/12167"
    ],
    [
      "-105141436805975748366562",
      "410179156429245433039211878735575030"
    ],
    [
      "-179369262832116806775606830/289",
      "2065706816417688350831704375501461650094/4913"
    ],
    [
      "482528797938179839881914",
      "-28323081641884004367139543755211098"
    ],
    [
      "6455253296606632615676474465090/6507601",
      "-13081723379415275642796963889713878081569537038/16600890151"
    ],
    [
      "188984785648092784299290",
      "188524863650845064420491293984766662"
    ]
  ],
  "submitter": "Roy van Rijn",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Roy van Rijn",
      "at": "2026-09-07 08:42:04"
    }
  ],
  "commentary": "This curve was found prospectively as the specialization t = 2818/1535 of an elliptic K3 family with generic Mordell–Weil rank 17.\r\n\r\nWe found 27 independent rational points on the specialized curve, proving rank at least 27 over Q; the exact rank is not currently known. The submitted equation is a globally minimal integral Weierstrass model. In this presentation, the specialization has 10 independent directions beyond the 17 generic sections.",
  "created_at": "2026-09-07 08:28:06",
  "updated_at": "2026-09-07 08:42:04"
}