{
  "id": 8,
  "curve_key": "45134376853266785419345109815961449:-9251161693101858048581020605248351326956236733759157",
  "ainvs": [
    "1",
    "0",
    "1",
    "-940299517776391362903023121165864",
    "10707363070719743033425295515449274534651125011362"
  ],
  "rank_lower_bound": 22,
  "naive_height": 239.38485678351597,
  "faltings_height": 17.87129795863137,
  "conductor": "22720638514787473197194583889675055980109503436060704437972911338086049759883790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "37",
    "47293",
    "270704849145149791",
    "60794657878864337775664712674231370427122734380997"
  ],
  "discriminant": "3680432205940761304587473756368167508478483727616134375685404923405185646725374901862332174937532900",
  "regulator": "12992022722213680254541.35531967258530327885791487307445312157323896249403008828342",
  "points": [
    [
      "32741153161482344264/3025",
      "-223089674587110979578532169697/166375"
    ],
    [
      "215521674613198983365/24649",
      "-6872949155061353554235704378947/3869893"
    ],
    [
      "637312541911044643/81",
      "-1420356190129296832193564087/729"
    ],
    [
      "-11906250919327880080/361",
      "-16580788535875788634285886853/6859"
    ],
    [
      "-136152345735493381/4",
      "-14482270545045735913281693/8"
    ],
    [
      "-27830298157016213012252/7134241",
      "72099692861364392796183359497454267/19055557711"
    ],
    [
      "4127671322151440",
      "2626107692045613116291646"
    ],
    [
      "6175679781777296",
      "2266254335997033124678449"
    ],
    [
      "12047255022287093",
      "1061993236525943920980477"
    ],
    [
      "416685837455186583191/32761",
      "5321268222786709669160311587369/5929741"
    ],
    [
      "149915813139075767108024/10220809",
      "8704326838108646949177663157917117/32675926373"
    ],
    [
      "58759417448623559/4",
      "2030968553150713398654657/8"
    ],
    [
      "237195157887349854919517/16024009",
      "-11477798111611307979707215505421441/64144108027"
    ],
    [
      "9568474434078537574436/687241",
      "319520556343135681977874272805086/569722789"
    ],
    [
      "1725892668710258675291/177241",
      "117378050663464845770966453025039/74618461"
    ],
    [
      "-35277008506980340471/1024",
      "48766027143946934186731674507/32768"
    ],
    [
      "-2752742763529705669/121",
      "6000532252185982381233585699/1331"
    ],
    [
      "-18552633109178014",
      "-4665466215824339436717966"
    ],
    [
      "-113251707338691187737649969/3304065361",
      "310152527894831470820009872373229341739/189920981015641"
    ],
    [
      "-7572001778163591251/729",
      "-86590661426506799357663502953/19683"
    ],
    [
      "-380526048554032285152211/11242609",
      "73081235744931307684790623068490233/37696467977"
    ],
    [
      "-1503889497722021588110681/42784681",
      "-160705885170116750151534640924719585/279854598421"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Fermigier (1997). A historical rank ≥ 22 record, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:11:50",
  "updated_at": "2026-07-01 22:29:41"
}