{
  "id": 3337,
  "curve_key": "6278004288:-497335052058624",
  "ainvs": [
    "0",
    "0",
    "0",
    "-130791756",
    "575619273216"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "naive_height": 67.68095393515803,
  "faltings_height": 3.3565442540542647,
  "conductor": "582587812371744",
  "bad_primes": [
    "2",
    "3",
    "23",
    "59",
    "139",
    "181",
    "193",
    "307"
  ],
  "discriminant": "54947892753143288082432",
  "regulator": "1528463.602983096154926302203366593987629158529196731",
  "points": [
    [
      "24484",
      "-3471404"
    ],
    [
      "167044/25",
      "-458428/125"
    ],
    [
      "60196/9",
      "160588/27"
    ],
    [
      "190756/25",
      "18491404/125"
    ],
    [
      "238276/25",
      "55176476/125"
    ],
    [
      "106849/16",
      "92561/64"
    ],
    [
      "63652/9",
      "1783180/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1242 (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 7 carries over. Torsion ℤ/2ℤ.",
  "created_at": "2026-09-26 21:02:32",
  "updated_at": "2026-09-26 21:02:32"
}