{
  "id": 3344,
  "curve_key": "187384144:-2565059193728",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-3903836",
    "2970119790"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "naive_height": 57.146013941190056,
  "faltings_height": 2.3678944864041487,
  "conductor": "21524842560",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "31",
    "41",
    "59"
  ],
  "discriminant": "32736594928440000",
  "regulator": "2902.72585066126569603990445913001542027321304397",
  "points": [
    [
      "897597/4",
      "-850362975/8"
    ],
    [
      "123597/4",
      "-43364775/8"
    ],
    [
      "463051/49",
      "-308681626/343"
    ],
    [
      "20197/4",
      "-2676875/8"
    ],
    [
      "877833/256",
      "-708164325/4096"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Rationally isogenous to curve#1912 (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 21:05:48",
  "updated_at": "2026-09-26 21:05:48"
}