{
  "id": 5768,
  "curve_key": "-473495716734532800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "9864494098636100",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 122.09675778458612,
  "faltings_height": 8.242970227023667,
  "conductor": "7784659505762115439670417856800",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "17",
    "73",
    "373",
    "1597",
    "1733"
  ],
  "discriminant": "-61433382203585445326591034915817409572088384000000",
  "regulator": "539546115308.2227678107577258964334042941801923307962280199",
  "points": [
    [
      "294863130",
      "5342783342700"
    ],
    [
      "2336380330/9",
      "120914682076700/27"
    ],
    [
      "74903479225/676",
      "27530001569131725/17576"
    ],
    [
      "479930316250/529",
      "334467762828391500/12167"
    ],
    [
      "1042343454650/961",
      "1068635114551872300/29791"
    ],
    [
      "3306761479945/2704",
      "6032980352544193125/140608"
    ],
    [
      "67719300988480/982081",
      "977161682134435650000/973242271"
    ],
    [
      "2136403949690000/57714409",
      "282753139262434145073000/438456365173"
    ],
    [
      "2371231270324170/14205361",
      "134361207812144428079700/53540005609"
    ],
    [
      "90969637814923520/57410929",
      "27491356948219585695789600/435002609033"
    ]
  ],
  "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 21:27:04",
  "updated_at": "2026-10-24 21:27:04"
}