{
  "id": 5494,
  "curve_key": "0:-271918944",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "314721"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 38.842029159698896,
  "faltings_height": 1.2944916724332034,
  "conductor": "33989868",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17"
  ],
  "discriminant": "-42789300987312",
  "regulator": "7813.0386775512668965362549792623606015321319",
  "points": [
    [
      "-22900301/447561",
      "127301577830/299418309"
    ],
    [
      "1382257999/11350161",
      "55688219664560/38238692409"
    ],
    [
      "-1630013039/24029604",
      "5997650980825/117793118808"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of hdeping’s ICARM curve #5171:\r\nhttps://elliptic-rank.icarm.cloud/curve/5171\r\n\r\nThe source model is y^2 = x^3 - 8497467. Applying the standard rational 3-isogeny and scaling by u = 3 gives y^2 = x^3 + 314721. 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 33989868, and minimal discriminant -42789300987312. Exact quadratic-character certification at 10 good primes gives an F2 matrix of rank 3, proving the three submitted points independent modulo torsion.",
  "created_at": "2026-10-22 12:09:22",
  "updated_at": "2026-10-22 12:09:22"
}