{
  "id": 1184,
  "curve_key": "12843280193202779015281:-1455713803525650851783078425165321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-267568337358391229485",
    "1684853939243502235524622982225"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    10
  ],
  "naive_height": 152.7216088714885,
  "faltings_height": 10.43373668653413,
  "conductor": "2914314327210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "29",
    "109",
    "11311"
  ],
  "discriminant": "-350454986086279087597351434974996124682603065833747251200000",
  "regulator": "14948.569527002120086478243892711430957094223",
  "points": [
    [
      "1721568508570417730/177235969",
      "113558364381360549042949855/2359542455297"
    ],
    [
      "3310921544308211650/194351481",
      "3898844358963966781829609635/2709453996621"
    ],
    [
      "496049677212875691106/53301418641",
      "342285594444255790379139807577/12305751823066311"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1091 and mapping all 3 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:38:40",
  "updated_at": "2026-09-23 21:38:40"
}