{
  "id": 5666,
  "curve_key": "70090383831796127246568276666576:-589429426153184071719645117119472796237730285400",
  "ainvs": [
    "0",
    "0",
    "1",
    "-1460216329829085984303505763887",
    "682209983973592675601441107777167588238113756"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 219.99096835879425,
  "faltings_height": 16.16372663908235,
  "conductor": "583945751773930214642842522548556249047256451031326349952152668504666354219282831713",
  "bad_primes": [
    "7",
    "17",
    "37",
    "41",
    "563723",
    "39486137",
    "145321395146795301244789402693108389357264661341034471363305966481"
  ],
  "discriminant": "-1792065862107248470345487631866561335694883897261978153431011754999954032466369108698540283",
  "regulator": "140787918997245571109305.3242597793791848312064927554224898431654765146258775541867",
  "points": [
    [
      "144223249040607",
      "-21785608414774053840666"
    ],
    [
      "761832742348841",
      "-3453811443751848676011"
    ],
    [
      "-631195951455979",
      "-36775248404812088601291"
    ],
    [
      "-112581433494125/9",
      "-714594643453179132417406/27"
    ],
    [
      "-1152871127501907",
      "-28867915908001569919659"
    ],
    [
      "1274284935438460583/11449",
      "27963877605840724207692847762/1225043"
    ],
    [
      "442070749758269",
      "11094296586164842128746"
    ],
    [
      "-1339058024096238",
      "15378265408069333264365"
    ],
    [
      "819330593815064",
      "-5985720277249250725989"
    ],
    [
      "1462040331612250",
      "40896412699734428832602"
    ],
    [
      "664206443926811",
      "-2313650359206731001895"
    ],
    [
      "950507964516882",
      "12369873968380675529709"
    ],
    [
      "673061157198080003137/1127844",
      "-5785098220244258146195464982877/1197770328"
    ],
    [
      "728221331851071",
      "-2242692465368166783591"
    ],
    [
      "57034444701897254/121",
      "-13219855800312250403289189/1331"
    ],
    [
      "738450560494416",
      "-2568330882493505330461"
    ],
    [
      "675088913957876",
      "2025475993839511631279"
    ],
    [
      "581641483938000",
      "5446179340732698001052"
    ],
    [
      "1021511139004344991/1225",
      "285729914908640659561610211/42875"
    ],
    [
      "211782720722947291/361",
      "35950610700838138639793666/6859"
    ],
    [
      "-727993343511873",
      "-36870313038762570483610"
    ],
    [
      "32413652612246",
      "25197481905099219144390"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 81/37 of the rank-17 fibration of X1008 given in curve#3589. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-24 02:40:09",
  "updated_at": "2026-10-24 02:40:09"
}