{
  "id": 6190,
  "curve_key": "799390900219971240615556829056:-714743811637723213709201170482749347287335296",
  "ainvs": [
    "0",
    "1",
    "0",
    "-16653977087916067512824100605",
    "827249781988100020096990567888085247623103"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 206.56099615767084,
  "faltings_height": 14.869360853071157,
  "conductor": "34984038809381284469645069641794389460",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "43",
    "47",
    "97",
    "101",
    "103",
    "199",
    "450391069",
    "803302864981"
  ],
  "discriminant": "-15797263861731380822963459960674246516339919161743551926196641403332823986764000000",
  "regulator": "21963761062.8355936252292182521870565345547111607971295955992",
  "points": [
    [
      "-110307304201799",
      "1149834233014007153250"
    ],
    [
      "69967143883801",
      "67348441681155612450"
    ],
    [
      "74667778773301",
      "5279080045784841450"
    ],
    [
      "75077577762373",
      "9746868410598431178"
    ],
    [
      "81181000661941",
      "101364983747156273130"
    ],
    [
      "94274364316681",
      "308358194976702999810"
    ],
    [
      "148328983460701",
      "1272965255184665715750"
    ],
    [
      "21455718353173189/289",
      "30244488478524700464150/4913"
    ],
    [
      "1567581698447213341/21316",
      "47222823388837019216314725/3112136"
    ],
    [
      "2455749072266293861/32041",
      "186056791715091988178240610/5735339"
    ],
    [
      "9299787670558257370009/120846049",
      "49292226331237030940428072973310/1328460616657"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = -748/2021 of the elliptic fibration of X648 given by:\r\ny^2 + (Lx+B)y = x^3,\r\nwhere\r\nL = 5098973881T^2 - 32101629380T + 51085836400,\r\nB = -2550648011199324171649113600T^5 - 231394683896910015292127210400T^4 + 1324630129545679262439545334000T^3 - 2330371426153230648960353010000T^2 + 1239686628515660725984584000000T.",
  "created_at": "2026-10-30 15:31:24",
  "updated_at": "2026-10-30 15:31:24"
}