{
  "id": 6192,
  "curve_key": "1299842244142030335451873413348196681:-1483194009776232536108323238165100748285020842798436421",
  "ainvs": [
    "1",
    "0",
    "1",
    "-27080046752958965321914029444754098",
    "1716659733537306173794629481425989867022234632842756"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 249.46758579756727,
  "faltings_height": 18.555755912439217,
  "conductor": "1088418986898974644212203666448533649270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "29",
    "31",
    "43",
    "47",
    "223",
    "229",
    "5431",
    "17419",
    "1135429",
    "45629533"
  ],
  "discriminant": "-2120483669548268809643076067393904874073985514018051267791303059465910159981149182843586888611375000000",
  "regulator": "53005270146.9199750663210902108056884347479359861089503860972",
  "points": [
    [
      "49591047396263045",
      "22264090455862809278866977"
    ],
    [
      "60756941362367645",
      "17194111000121477123512977"
    ],
    [
      "87613088443631717",
      "4076264920600935345829569"
    ],
    [
      "345107777068479170",
      "182956952458782711336911352"
    ],
    [
      "-1007659500004506347536/5329",
      "3398597639188406867601180863043/389017"
    ],
    [
      "-21870125232552924595/2809",
      "6535387967258597444288714969829/148877"
    ],
    [
      "2234109198068729477/16",
      "1641486554202794236752178887/64"
    ],
    [
      "16866764003067896600/121",
      "33944626528905167535739397337/1331"
    ],
    [
      "113424579416482279730/5929",
      "15851670445308045341079643598616/456533"
    ],
    [
      "427667385634837379620/4761",
      "982451870449485627362240311043/328509"
    ],
    [
      "581255345444249336165/529",
      "13864737657240813805157324868879/12167"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 2914/145 of the elliptic fibration of X648 given by:\ny^2 + (Lx+B)y = x^3,\nwhere\nL = 5098973881T^2 - 32101629380T + 51085836400,\nB = -2550648011199324171649113600T^5 - 231394683896910015292127210400T^4 + 1324630129545679262439545334000T^3 - 2330371426153230648960353010000T^2 + 1239686628515660725984584000000T.",
  "created_at": "2026-10-30 15:40:31",
  "updated_at": "2026-10-30 15:40:31"
}