{
  "id": 5493,
  "curve_key": "0:-224726400",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "260100"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 38.4607884404816,
  "faltings_height": 1.2627216124984284,
  "conductor": "7022700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17"
  ],
  "discriminant": "-29225668320000",
  "regulator": "6234.4967690131582745846969658467835553102560",
  "points": [
    [
      "-16081811/471969",
      "152269585237/324242703"
    ],
    [
      "14417749/1096209",
      "587897217593/1147730823"
    ],
    [
      "-1343054591/21288996",
      "9328022857727/98227427544"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of hdeping’s ICARM curve #5170:\r\nhttps://elliptic-rank.icarm.cloud/curve/5170\r\n\r\nThe source model is y^2 = x^3 - 7022700. Applying the standard rational 3-isogeny and scaling by u = 3 gives y^2 = x^3 + 260100. The three submitted points are exact transported points.\r\n\r\nPARI/GP 2.17.4 returned rank bounds [3,3], torsion Z/3Z, conductor 7022700, and minimal discriminant -29225668320000. Exact quadratic-character certification at 11 good primes gives an F2 matrix of rank 3, proving the three submitted points independent modulo torsion.",
  "created_at": "2026-10-22 12:06:36",
  "updated_at": "2026-10-22 12:06:36"
}