{
  "id": 5703,
  "curve_key": "-427320464064:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "8902509668",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 80.34240021003177,
  "faltings_height": 4.763440429144138,
  "conductor": "937925188033532192",
  "bad_primes": [
    "2",
    "13",
    "29",
    "233",
    "1949"
  ],
  "discriminant": "-45156194597812520442313608040448",
  "regulator": "16575465.63976003275691686038856450608643594496944406",
  "points": [
    [
      "322624",
      "190926384"
    ],
    [
      "984064/9",
      "1289403584/27"
    ],
    [
      "628849/144",
      "10785904649/1728"
    ],
    [
      "5414929/36",
      "14874446951/216"
    ],
    [
      "52243984/441",
      "482752641176/9261"
    ],
    [
      "59428681/196",
      "479805022437/2744"
    ],
    [
      "134467216/1681",
      "2411237475192/68921"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5669:\r\nhttps://elliptic-rank.icarm.cloud/curve/5669\r\n\r\nRubinstein reports rank 7 proved, with seven independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 - 2225627417*x.\r\n\r\nWriting A = -2225627417, the rational 2-isogeny\r\n(x,y) -> (x + A/x, y*(x^2-A)/x^2)\r\ngives the global minimal model y^2 = x^3 + 8902509668*x.\r\n\r\nThe seven submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 937925188033532192, equal to the source conductor.",
  "created_at": "2026-10-24 14:02:05",
  "updated_at": "2026-10-24 14:02:05"
}