{
  "id": 5489,
  "curve_key": "0:-157532256",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "182329"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 37.75028159052261,
  "faltings_height": 1.2035127083351795,
  "conductor": "19691532",
  "bad_primes": [
    "2",
    "3",
    "7",
    "61"
  ],
  "discriminant": "-14361349352112",
  "regulator": "306.33552459131951968651330181861590996962514",
  "points": [
    [
      "-45",
      "302"
    ],
    [
      "57/4",
      "3443/8"
    ],
    [
      "-199335/5476",
      "148388477/405224"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of hdeping’s ICARM curve #5166:\r\nhttps://elliptic-rank.icarm.cloud/curve/5166\r\n\r\nFor the source model y^2 = x^3 - 4922883, the standard 3-isogenous Mordell model is y^2 = x^3 + 132917841. Rational scaling by u = 3 gives the minimal integral model y^2 = x^3 + 182329. The three submitted points are exact images under this isogeny and scaling.\r\n\r\nPARI/GP 2.17.4 returned rank bounds [3,3], rational torsion Z/3Z, conductor 19691532 and minimal discriminant -14361349352112. Exact quadratic-character certification at 12 good primes gives an F_2 matrix of rank 3, proving the three submitted points independent modulo torsion.",
  "created_at": "2026-10-22 11:48:29",
  "updated_at": "2026-10-22 11:48:29"
}