{
  "id": 3338,
  "curve_key": "9234599488:-399154120501760",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-192387489",
    "462048064929"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 68.83866924220374,
  "faltings_height": 3.791184718518509,
  "conductor": "144443213376",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "31",
    "71",
    "193"
  ],
  "discriminant": "363531581098062408489959424",
  "regulator": "8067.58113245862448473842897933880071228812990674",
  "points": [
    [
      "-1487",
      "863040"
    ],
    [
      "67677/4",
      "-11454345/8"
    ],
    [
      "5937/16",
      "40004415/64"
    ],
    [
      "-723/4",
      "5638815/8"
    ],
    [
      "679137/49",
      "232087680/343"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1644 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-26 21:02:52",
  "updated_at": "2026-09-26 21:02:52"
}