{
  "id": 4063,
  "curve_key": "1733298607642212091483784870404743699561502573487841441:-1971554511010161018861650648224677956977436414141285303280769305291437845296475761",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-36110387659212751905912184800098827074197970280996697",
    "2281891795150649327386169740769122327971517159511941226970041612636804891194169"
  ],
  "rank_lower_bound": 20,
  "torsion": [
    2
  ],
  "naive_height": 374.66886397303347,
  "faltings_height": 29.211712575023153,
  "conductor": "3837790555226969705537890168396950553913036309626451197868514544063254214128052127345730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "47",
    "79",
    "157",
    "197",
    "239",
    "283",
    "331",
    "479",
    "1381",
    "1511",
    "1531",
    "1811",
    "4111",
    "8783",
    "16943",
    "20107",
    "32653",
    "36901",
    "135409",
    "17470571",
    "220570313"
  ],
  "discriminant": "764099262650684849672633829624708925630842407000252083204662584628011249477802993841592848621305996923811493921258105978769784891816631847192444861929881600000",
  "regulator": "12746766710868894028145.8426513966906738917935723267104903472851657574773564092",
  "points": [
    [
      "74761088215882442469470503",
      "9803601168587528224069543093705673388"
    ],
    [
      "74761908203915691129124777",
      "8958233209269883027798539821715513286"
    ],
    [
      "74471054396781312964779927",
      "75663714715314606043009805241037293436"
    ],
    [
      "141630143524136830589989287",
      "92440650670301906282230240106703928876"
    ],
    [
      "42746352782766638527494177",
      "903555602703044653541406892373896539886"
    ],
    [
      "51909761285723148437934327",
      "739788784013998398858543191240343086236"
    ],
    [
      "52114929551846244384269187",
      "735896634600698034599577237565217561836"
    ],
    [
      "66819099337371668547396327",
      "409098518244791269037965449229073619436"
    ],
    [
      "68556018206266656188321767",
      "358490900412051730877504861438419048236"
    ],
    [
      "70289292655657169976948999",
      "301642819013902440410420658168547019692"
    ],
    [
      "72100996912140139915055527",
      "230472892823935346797320643358014779436"
    ],
    [
      "73469951896633085388553527",
      "159505306557649240649224573160413747036"
    ],
    [
      "-2724383059560738872997053",
      "1542805918602807495125878604135984595436"
    ],
    [
      "145071022257426966091155879",
      "310528367097348217902277072722314737708"
    ],
    [
      "147484236401516359735573479",
      "405212240256504121123842060215435672812"
    ],
    [
      "148103003328569733159707287",
      "427083361865705244821618596022079731836"
    ],
    [
      "149331454879852444096263207",
      "468560672663528084870974283995920440236"
    ],
    [
      "18783227520944600325938167",
      "1268955898187418215071825469314267229596"
    ],
    [
      "19592694610079009358035847",
      "1257741275984062729509614577388630400716"
    ],
    [
      "162163751185882459144920162763/9",
      "65299011007905183468793630021953775696571872/27"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = -9229/194873 of the rank-9 fibration of X588 given by:\ny^2 + (1744T^2 - 8532T - 607)xy = x(x + (63T - 109)(647T - 41)(7T - 2)(T + 95))(x + 9(111T - 40)(383T - 38)(87T - 16)(T + 5)).",
  "created_at": "2026-10-08 22:48:03",
  "updated_at": "2026-10-08 22:48:03"
}