{
  "id": 5767,
  "curve_key": "118373929183633200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2466123524659025",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 117.93787470122645,
  "faltings_height": 7.896396636743694,
  "conductor": "7784659505762115439670417856800",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "17",
    "73",
    "373",
    "1597",
    "1733"
  ],
  "discriminant": "959896596931022583227984920559647024563881000000",
  "regulator": "394116957.8584534461729420934232530345465158453840732125785",
  "points": [
    [
      "-34789975",
      "209018169800"
    ],
    [
      "-7465975",
      "134148638800"
    ],
    [
      "69190025",
      "400748624800"
    ],
    [
      "75272855",
      "490779014600"
    ],
    [
      "145811295",
      "1655444235900"
    ],
    [
      "35356102775",
      "6648078716988800"
    ],
    [
      "-35088589305/3481",
      "31707218915641500/205379"
    ],
    [
      "739240121/4",
      "19359959528869/8"
    ],
    [
      "1036880320/9",
      "30127205747800/27"
    ],
    [
      "26676906039/361",
      "3226636995631812/6859"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Rank 10, proved: 10 independent points listed, matching the 2-descent upper bound. Torsion Z/2. Member of the family y^2 = x^3 + a x.",
  "created_at": "2026-10-24 21:26:53",
  "updated_at": "2026-10-24 21:26:53"
}