{
  "id": 5695,
  "curve_key": "-21161657183522064:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "440867857990043",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 112.77290194690738,
  "faltings_height": 7.465982240550439,
  "conductor": "6219662982679319087228388539168",
  "bad_primes": [
    "2",
    "11",
    "17",
    "41",
    "61",
    "73",
    "157",
    "233",
    "353"
  ],
  "discriminant": "-5484098993187586645132713663806424394919008448",
  "regulator": "435957088.5039029740197211270410202618093952642870808004877",
  "points": [
    [
      "11692175",
      "82177282770"
    ],
    [
      "25561327",
      "167243726562"
    ],
    [
      "56307893",
      "450946729434"
    ],
    [
      "89158149",
      "864893484066"
    ],
    [
      "280466527",
      "4710154854438"
    ],
    [
      "1261214284",
      "44796439546254"
    ],
    [
      "24994871/25",
      "2627310870294/125"
    ],
    [
      "487287337/36",
      "19852573396717/216"
    ],
    [
      "6678702913/784",
      "1451796403119201/21952"
    ],
    [
      "2357582128289/75076",
      "4354569712474069161/20570824"
    ]
  ],
  "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 13:20:39",
  "updated_at": "2026-10-24 13:20:39"
}