{
  "id": 3336,
  "curve_key": "9136729:27323348707",
  "ainvs": [
    "1",
    "1",
    "0",
    "-190348",
    "-31703558"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "naive_height": 48.08343900574561,
  "faltings_height": 1.8748958389564907,
  "conductor": "1364469990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "59",
    "3121"
  ],
  "discriminant": "9355948312821630",
  "regulator": "869.557511437825625326700228479218515443036894958",
  "points": [
    [
      "-273",
      "227"
    ],
    [
      "-267",
      "551"
    ],
    [
      "-231",
      "200"
    ],
    [
      "783",
      "16931"
    ],
    [
      "6867",
      "564491"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1249 (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.",
  "created_at": "2026-09-26 21:02:22",
  "updated_at": "2026-09-26 21:02:22"
}