{
  "id": 758,
  "curve_key": "223642008266390217243210142691425:-3345700920981407535565322865681336640424818155025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4659208505549796192566877972738",
    "3872339028913665740859155632055568027325930692"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 223.46352135647527,
  "faltings_height": 16.359522212220625,
  "conductor": "23789261559055379338105234248315974632795330743806015189919339103950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "37",
    "43",
    "89",
    "1051",
    "154609219",
    "707424629",
    "644635416755471",
    "3599574785289150212183"
  ],
  "discriminant": "-4683076378200201054706808777044542971578135645187890483155129326284455211358884882821120000",
  "regulator": "93675267828215863394.6173115996625124458830483395767028481609434647588793529193",
  "points": [
    [
      "-245908406229948",
      "-70733353065492736071666"
    ],
    [
      "58011663190477176/121",
      "-55659874201641240867863766/1331"
    ],
    [
      "731292312063258",
      "-29260594129503168993150"
    ],
    [
      "1689332227554852",
      "-28678869920446921176786"
    ],
    [
      "788286571512899976/625",
      "-23430593672510390284818726/15625"
    ],
    [
      "1276594700307222",
      "-2208371861138495771646"
    ],
    [
      "474704254692502272/361",
      "-30206866539963857400281574/6859"
    ],
    [
      "-1191510361576668",
      "-87933216243133624529106"
    ],
    [
      "61170591518809938/49",
      "-408356460720165166325388/343"
    ],
    [
      "1378002767490852",
      "-8283401645920574826066"
    ],
    [
      "3569640265334309292/361",
      "-6595472578598442958043906334/6859"
    ],
    [
      "2765176858041192",
      "-110144938785972987955986"
    ],
    [
      "4961997927393372",
      "-320818967190758419007346"
    ],
    [
      "1665296047336932",
      "-27048008396916245539026"
    ],
    [
      "438315503443445862972/326041",
      "-1152900711987926313995881154046/186169411"
    ],
    [
      "3111265842932772",
      "-139618334094080356686546"
    ],
    [
      "88623450578371767051935518307748/76975946096924449",
      "-124934608766501342877095240680543833070918102962/21356621616408019844113457"
    ],
    [
      "91113527945731327088505199900565478318/75058087492735178646049",
      "-47208398897612300480064259024690292721752420382578364432/20563462398661982316313519053716657"
    ],
    [
      "179582859760718634822/130321",
      "-389703570061702450537962908136/47045881"
    ],
    [
      "75400529481812854437984/21836929",
      "-17362934646071823485113248983641842/102043969217"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization at T = -2/9 of the rank-16 fibration of X948 described by wgxli for ICARM #625. Starting from 4 elementary polynomial sections, an independent rational-point search yields 20 points with an exact independence certificate, proving rank >= 20.",
  "created_at": "2026-09-18 02:14:59",
  "updated_at": "2026-09-18 02:14:59"
}