{
  "id": 5737,
  "curve_key": "-76059612140927184:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1584575252935983",
    "0"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 116.61088139404431,
  "faltings_height": 7.785813861145184,
  "conductor": "8927568825660922670440875293472",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "37",
    "43",
    "53",
    "113",
    "317",
    "757"
  ],
  "discriminant": "-254635283340450958665869105455822142425568453568",
  "regulator": "2974216967.438898461697158073412338948877172964727597181687",
  "points": [
    [
      "16224201",
      "173144673072"
    ],
    [
      "40803057",
      "364126480668"
    ],
    [
      "108127327",
      "1198127108332"
    ],
    [
      "132840631",
      "1598338472192"
    ],
    [
      "940951/9",
      "347523314732/27"
    ],
    [
      "1994337/4",
      "224879445783/8"
    ],
    [
      "36729583/9",
      "2182616398864/27"
    ],
    [
      "20638986361/100",
      "3019699160200891/1000"
    ],
    [
      "454423645809/256",
      "306408321472446711/4096"
    ],
    [
      "596103993639/11449",
      "579338976057265116/1225043"
    ]
  ],
  "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 18:03:09",
  "updated_at": "2026-10-24 18:03:09"
}