{
  "id": 736,
  "curve_key": "2991874338482572413913786531281:-5179210397414405729576876213946606701048731929",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-62330715385053591956537219402",
    "5994456478488911103022452992502858001259401"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 210.52196359290556,
  "faltings_height": 15.30892417061931,
  "conductor": "528231522282148305732318171943623605900920769594482376831197710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "43",
    "59",
    "23011943137",
    "25265118093587",
    "1759892540399429283515554272293"
  ],
  "discriminant": "-24895544437583552594644825153545076278982533771778054578056326482615597253926912000000",
  "regulator": "160528730390667013.1537921800732385331731274803042248452855625597056274461987",
  "points": [
    [
      "-160763371664111",
      "-3443841573927531887881"
    ],
    [
      "42721767645841",
      "-1846497177738479971081"
    ],
    [
      "108718858323769",
      "-709201263202549497241"
    ],
    [
      "140774590434241",
      "-98356193267497121881"
    ],
    [
      "141673259686351",
      "-86192418544744510951"
    ],
    [
      "41021011752661999/289",
      "-407881460392446186720503/4913"
    ],
    [
      "810299143053652051/5476",
      "-42905988999578653555163999/405224"
    ],
    [
      "152283068712571",
      "-184413969899801402641"
    ],
    [
      "159979187135461",
      "-342404924486269771141"
    ],
    [
      "77647912115897341/441",
      "-6404459071744715324981261/9261"
    ],
    [
      "204427092487241",
      "-1339950442381527154361"
    ],
    [
      "380301010985155",
      "-6106760680037678842273"
    ],
    [
      "3459095905080691",
      "-202927724403572519020531"
    ],
    [
      "4194869565495001",
      "-271221966834037704844801"
    ],
    [
      "6071322492482479",
      "-472675706603494827014569"
    ],
    [
      "27597984435565489",
      "-4584567168898733491723081"
    ],
    [
      "98018114961523601",
      "-30687259965939258848536201"
    ],
    [
      "143842122625601",
      "-69624785948937034201"
    ],
    [
      "143936585219281",
      "-69476557307295291721"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=4/3 of the family identified by wgxli in the commentary to curve #302. Starting from 17 reconstructed generic sections, minimized quartic searches produced a set of 19 points certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 17:21:34",
  "updated_at": "2026-09-16 17:21:34"
}