{
  "id": 65,
  "curve_key": "58683989082049435979413878577717203009129601:-452707874380980964751123855943852496111823697994336414045572254401",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1222583105876029916237789137035775062690200",
    "523967447200209449943328506898413682821590945806099349816040000"
  ],
  "rank_lower_bound": 25,
  "naive_height": 302.35621581434873,
  "faltings_height": 23.045960193031338,
  "conductor": "3421625153333343825198002959770328244842456471613462044687992344664286334910845403447307652180335890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "157",
    "283",
    "72551",
    "895613",
    "39466373175449369221626360280383658386480681928740709773906484427935361743867171"
  ],
  "discriminant": "-1648077180048519919196851388268507997232089165506048976474499224670899793965899322864689351309245989194390271909250018304000000",
  "regulator": "724084252210012759383791369.1859440608064513839867489159651105029300072050018474263574137",
  "points": [
    [
      "641919671491882025200",
      "1917622583611100541324074905000"
    ],
    [
      "594994690844383471600",
      "2678847964182260740553494589800"
    ],
    [
      "208196841608040479152",
      "16686940720261011217265226309352"
    ],
    [
      "-740361154329309511040",
      "-31989105845069848078376802650600"
    ],
    [
      "804899774308127940400",
      "7834276239548635107854922077800"
    ],
    [
      "77301598762979192560",
      "20734554180656765176390619976040"
    ],
    [
      "702911299694560038040",
      "-3449260992056554312601103761600"
    ],
    [
      "915485567326094606800",
      "-13114547973847689345711009896600"
    ],
    [
      "-26293910519288470100",
      "-23581682704464936496514064216200"
    ],
    [
      "709908819594746168740",
      "-3717262868674905037217938483100"
    ],
    [
      "875280814115630686150",
      "11154863867288165850338319192550"
    ],
    [
      "1643784276034119529840",
      "54367762877007597564101217327400"
    ],
    [
      "2310209163245804946160",
      "100146314980252246302935050670440"
    ],
    [
      "1909368489723249677080",
      "-71767455269710117770413293033280"
    ],
    [
      "673388810420663671600",
      "-2458352439913512016092058261400"
    ],
    [
      "-1225141077322557861200",
      "13524179089651555542230916989800"
    ],
    [
      "641884454793213323650",
      "1917498326574315724474707751300"
    ],
    [
      "1779583257516825231520",
      "63119495622551336426454649548280"
    ],
    [
      "1336811684405040135250",
      "35757154248294043850600009373700"
    ],
    [
      "591774410894432534320",
      "-2776985009258775118824482266520"
    ],
    [
      "4566516049692282828100",
      "300278030461559541447358362839800"
    ],
    [
      "-499965890434284752520",
      "-31784318126596227394232274064800"
    ],
    [
      "1239030190644321769050",
      "-30187812602932900034742078815100"
    ],
    [
      "3417029330608564213375/4",
      "-81177702701038029224605519995775/8"
    ],
    [
      "9868611464482118831434/25",
      "1267809878380229048466900915382388/125"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Andrej Dujella rank-record table \"Rank >= 25\", Elkies (2006). The page lists this curve y^2 + xy = x^3 - 1222583105876029916237789137035775062690200*x + 523967447200209449943328506898413682821590945806099349816040000 and the 25 independent points submitted here.",
  "created_at": "2026-05-29 04:45:51",
  "updated_at": "2026-07-01 22:29:39"
}