{
  "id": 5495,
  "curve_key": "0:-382082400",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "442225"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 39.52229370023153,
  "faltings_height": 1.351180384144256,
  "conductor": "15920100",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19"
  ],
  "discriminant": "-84483194670000",
  "regulator": "541.66284309937481453903836858269729480394857",
  "points": [
    [
      "11",
      "666"
    ],
    [
      "42919/441",
      "10816028/9261"
    ],
    [
      "-285409/9409",
      "587462436/912673"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of hdeping’s ICARM curve #5172:\r\nhttps://elliptic-rank.icarm.cloud/curve/5172\r\n\r\nThe source model is y^2 = x^3 - 11940075. Applying the standard rational 3-isogeny and scaling by u = 3 gives y^2 = x^3 + 442225. 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 15920100, and minimal discriminant -84483194670000. 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 12:11:37",
  "updated_at": "2026-10-22 12:11:37"
}