{
  "id": 6194,
  "curve_key": "191213659893528844574967601:-2644169145033719008162521466415048111401",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3983617914448517595311825",
    "3060380954899805772769306913365955625"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 181.54635103974104,
  "faltings_height": 12.782901150607996,
  "conductor": "11484664266941817735462405540582990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "61",
    "97",
    "101",
    "139",
    "353",
    "5394979",
    "753623680363"
  ],
  "discriminant": "-202384434010796172350747665468852382714955388714799102819585828352000000",
  "regulator": "130502129.6120305188307890935104175685147987762726356743609",
  "points": [
    [
      "-1633343422700",
      "2282443796152497025"
    ],
    [
      "-1533731033990",
      "2358461387246441275"
    ],
    [
      "817037042460",
      "592477648843274025"
    ],
    [
      "1123303270090",
      "54455749379036635"
    ],
    [
      "1137030917650",
      "29706105259612675"
    ],
    [
      "1147650719200",
      "12338258788910125"
    ],
    [
      "1320384483250",
      "320080625988805675"
    ],
    [
      "14036889363082",
      "52085412509210006491"
    ],
    [
      "28721691700354/25",
      "1357926313533705023/125"
    ],
    [
      "1577756581634770/1369",
      "443361693168252439975/50653"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = -5185/353 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 15:40:45",
  "updated_at": "2026-10-30 15:40:45"
}